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04c89e91af3d0abd0f93e9dace90a3f8899d1d60 | subsection | 102 | 104 | Symbolic finite automata. | This is probably due to the use of the removal of simulation smaller transitions, which does not have a meaningful counterpart when working with bisimulations.
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5957810277622cc32494d239e39ba8b2947b7429 | subsection | 103 | 104 | Symbolic finite automata. | Fig.~\ref {app:fig:simbisim-time-iteration} shows the overall time needed by the iterative reduction process, Fig.~\ref {app:fig:simbisim-time-once} then the time taken by the first iteration---essentially the time taken by computing the simulation preorder or the bisimulation equivalence.
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5c8d9f1e67ea29e8f7404c9da62551c1f7a66579 | abstract | 0 | 24 | Abstract | This paper presents results from the development and evaluation of a
deductive verification benchmark consisting of 26 unmodified Linux kernel
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4c26f69c1c6ed985c858e43b5fe04b0d913cb999 | subsection | 1 | 24 | Body | 0pt10pt plus 0pt minus 2pt8pt plus 0pt minus 2pt0pt8pt plus 0pt minus 1pt6pt plus 0pt minus 1ptlstlistingchapterDeductive Verification of Unmodified Linux Kernel Library FunctionsDenis Efremov1,2 Mikhail Mandrykin2 Alexey Khoroshilov1,2,3,4
National Research University Higher School of Economics, Moscow, RussiaIvanniko... | {
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eb0db5b3b05aa3131e3a3925788b5002048151b0 | subsection | 2 | 24 | Body | As explained in describing the design choices behind the Jessie tool, byte-level block memory model in principle allows us to express common but non-standard C code fragments, such an implementation of the function memmove, while retaining the ability to detect use-after-free memory safety errors and potential pointer... | {
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95ebd5b828690d1c2fff0a8cc361a10d7490fb9f | subsection | 3 | 24 | Body | Consider the following property of this function: two valid pointers from different blocks cannot have the same address. It cannot be expressed as a logical proposition using the current Jessie theory since this would involve bounded existential quantification over all possible reachable states of the corresponding all... | {
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edf6c3560b55384cd7f639e62a7a5e68c36b58a2 | subsection | 4 | 24 | Body | Second, it implements a number of normalizing code transformations that rewrite nested structures and addressed fields of simple types into pointers to separately allocated structures or values of the corresponding type (the transformations are described in ). This allows us to express the addresses of nested objects i... | {
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28addf7a0481f02607e5c4c7a7f839d989b46fd8 | subsection | 5 | 24 | Body | For these purposes Jessie implements modulo integer model, which precisely models values of integral types as bitvectors.Unfortunately, the integer model in Jessie can only be chosen once for the entire program analyzed using the corresponding pragma. In practice, however, it is desirable to be able to choose the appro... | {
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616203ed40508de344567e8e8d0f5c4179a8fa52 | subsection | 6 | 24 | Body | The operation & in logic is encoded as bitwise conjunction with the same type as +%. The relation < in logic is encoded as either bitwise or integer relation depending on the type of arguments. The bitwise relations is augmented with an axiom relating it to the integer one. The operation a \mathop {\texttt {+}} b in co... | {
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037cf38ad0e3495bd8101d1253356ebbe56103e1 | subsection | 7 | 24 | Body | This can be potentially addressed by either adding some preliminary instantiation step or implementing similar support for the necessary operations as an SMT theory directly in the solver (by converting axioms into inference rules of the theory).Lastly, let's demonstrate some practical capabilities of this integer mode... | {
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3d0ca66921994a186b8421ecab5c1122a4504731 | subsection | 8 | 24 | Introduction | Deductive verification is one of the most rigorous techniques to ensure software satisfies its requirements. In spite of significant advances in tool support, it still requires deep user involvement in the verification process to provide manual guidance (e. g., to specify the contract of each function and to identify l... | {
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bb9f63f0609c11ceb6b6b69b67e656bbfce9758f | subsection | 9 | 24 | Related Work | Since the deductive verification tools, WP and Jessie are mature enough there are many examples where these tools were applied for verification of real-life software. In 12 string functions from OpenBSD were examined, using Jessie as a deductive verification plug-in. The correctness of 7 functions was fully proved (al... | {
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7f6d5a1e136a4065afa85a227f7085389d77d36f | subsection | 10 | 24 | Related Work | The authors regularly update the document with new specifications and functions, bug-fixes, etc. This project started in 2009. The document contains a number of fully verified functions. They were proved with Alt-Ergo, CVC3, CVC4, Z3, and EProver solvers. Authors use the WP deductive verification plugin.GrammaTech repo... | {
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50e992b8d5d5204e93e04abefd45c6139459a329 | subsection | 11 | 24 | ACSL | ACSL is designed to be suitable for specifying safety properties of C programs, including contract specifications (pre- and postconditions) and assertions with arbitrary predicates on one or several memory states. The language also supports the specification of function frame conditions, axiomatic theories and addition... | {
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1770cb359137a2605a46a6a0569b4d84d3f7bf1b | subsection | 12 | 24 | ACSL | In both of those cases, the corresponding operation (type cast or decrement) discards some parts of the bitwise representation of the argument (higher bits of the int value and the sign bit correspondingly), which corresponds to the intention of the programmer. To distinguish those intentionally overflowing operations,... | {
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8d00fcbaff78acc27e1dbde465cbedec77f74da9 | subsection | 13 | 24 | Region separation in | Since there are two deductive verification plugins for the Frama-C platform, we had to make a choice between Jessie and WP. While there may be many arguments for choosing a more up-to-date and actively maintained WP plugin, which, among others, has capabilities for bitwise modelling of in-memory data representation and... | {
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28fb53afeeb236eb845ec408f19dc062572add1e | subsection | 14 | 24 | Formal Specifications | We were guided by several techniques in the development of specifications: the use of excessive specifications (explicit specifications and specifications that establish the correspondence with a logical function), the development of specifications based on source code, and the context of function calls.The results des... | {
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11c6c99784aff163e5320af28a6cc7e0d0b12c78 | subsection | 15 | 24 | Formal Specifications | We tried to maximally weaken the preconditions and strengthen the postcondition in order to test the instruments of deductive verification, the expressiveness of the ACSL language, and the capabilities of solvers.[caption=strncmp contract,label=lst:strncmpverker,captionpos=b,breaklines=false,breakautoindent=false,linew... | {
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faa0840365f64e8353c2e8e143efe78541f63b3a | subsection | 16 | 24 | Logic Functions | The specifications are redundant for some functions. In fact, they describe a function's behavior in two different ways. For example, strlen specification consists of the usual functional requirements and the requirement for the correspondence between the returned value and the logical function. This approach is motiva... | {
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"Denis Efremov",
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64bb2269e7ac0080d53bebd50cb1a235517c4601 | subsection | 17 | 24 | Open Issues | At the specification level, the authors faced many problems related to significant inaccuracies in the modeling of pointer operations, as well as the insufficient level of ACSL language support by the tools.Thus, for the memmove function, there is the VC, which states that the dest and src pointers should lie in the sa... | {
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bac62197aef3efb889ff4ddf0454c61a30a5024f | subsection | 18 | 24 | Open Issues | This drawback prevents the explicit definition of the logical functions for skipspaces, strcspn, strpbrk, and strspn.Functions from the file ctype.h (isspace, isdigit, isalnum, isgraph, islower, ...) are defined as macros that operate on the array _ctype of 256 bytes, which specifies the belonging of each character to ... | {
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329d6fcc661dc6fdce9e3bc7bfdf4fee4fbe37f9 | subsection | 19 | 24 | Evaluation of Solvers | AstraVer translates Frama-C's internal representation into the program model in WhyML , based on the memory model and semantics of operations with integers. The Why3 tool generates VCs for a WhyML program and converts them into an input for solvers. Why3 supports a number of solvers, such as Alt-Ergo, CVC3, CVC4, Z3, S... | {
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ca5652cb6e4434539f6afcaa78ca6aa258dba38c | subsection | 20 | 24 | VC transformation strategy | To put all solvers in similar conditions all VCs were transformed by Why3 using the following strategy:Split goal by conjuncts (split_goal_wp) repeatedly until fixed point.
Inline definition of all logical symbols (inline_all).
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7b0c0f8572158a857ed3b64d0e146ee6e907e183 | subsection | 21 | 24 | Statistics | table:bench presents the results of the evaluation. The first column contains the target function name the second one includes the number of VCs generated (safety and behavioral) after application of the transformation strategy. The rest of the table presents solver statistics: the amount of discharged VCs and the aver... | {
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} | 10.1007/978-3-030-03421-4_15 | 1809.00626 | Deductive Verification of Unmodified Linux Kernel Library Functions | [
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3c4eeb826127d7186a5a7f8f2a7314c420dd90c7 | subsection | 22 | 24 | Discussion | All VCs except one for memmove are successfully discharged by at least one of the solvers. The best result was achieved by Alt-Ergo and CVC4. This is expected as those solvers were most extensively used during the development and testing of the toolset.CVC4 1.5 discharged the greatest number of VCs, while Z3 required t... | {
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c07a1528714184297c00371252f14985bedd47a1 | subsection | 23 | 24 | Conclusion | This paper presents results from the development and evaluation of a deductive verification benchmark consisting of 26 unmodified Linux kernel library functions implementing conventional memory and string operations. Formal contracts of the functions were extracted from their source code and were represented in the for... | {
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10e4ae3f9ec54ac04484c1fe172a7f9d4d5d5506 | abstract | 0 | 70 | Abstract | In this paper, we set up a rational homotopy theory for operads in simplicial
sets whose term of arity one is not necessarily reduced to an operadic unit,
extending results obtained by the author in the book "Homotopy of operads and
Grothendieck-Teichm\"uller groups". In short, we prove that the rational
homotopy type ... | {
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} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
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9e31fe70364b4ee3b2a059f3766c82e905b750b8 | subsection | 1 | 70 | Introduction | In , the author proved that the Sullivan model for the rational homotopy theory of spaces
admits an extension to the category of operads in simplicial sets \operatorname{{P}} whose term of arity one
is reduced to a one-point set \operatorname{{P}}(1) = *.
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59d5706363f566ae7185e70356369798585703c6 | subsection | 2 | 70 | Introduction | This property simplifies the definition of our model.
In particular, we prove in that the category of Hopf cochain dg-cooperads
such that \operatorname{{A}}(1) = \operatorname{\mathbb {Q}} inherits a model category structure with the quasi-isomorphisms of Hopf cochain dg-cooperads
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5ebb0bf41ae327e371038f970b381aaf3c4f7e1d | subsection | 3 | 70 | Introduction | To be explicit, we have the identity X^{\operatorname{\mathbb {Q}}} = \operatorname{\mathtt {L}}\operatorname{\mathtt {G}}(\operatorname{\mathtt {\Omega }}^*(X)), where we use the notation \operatorname{\mathtt {L}}\operatorname{\mathtt {G}}(-)
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ebada0c7c5c2ad20c2fb2fc8946d89a32731ee7d | subsection | 4 | 70 | Introduction | We explicitly have \operatorname{\mathtt {G}}(\operatorname{{A}})(r) = \operatorname{\mathtt {G}}(\operatorname{{A}}(r)), for each r>0,
for any \operatorname{{A}}\in \operatorname{\mathit {dg}}^*\operatorname{\mathcal {H}\mathit {opf}}\operatorname{\mathcal {O}\mathit {p}}_{01}^c.
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7ab1b121d97c0ffb4c783d23b9dc5005a92cc962 | subsection | 5 | 70 | Introduction | This result implies that our operadic rationalization functor \operatorname{{P}}^{\operatorname{\mathbb {Q}}}
reduces to the Sullivan rationalization of spaces
arity-wise. We explicitly have a weak-equivalence of simplicial sets \operatorname{{P}}^{\operatorname{\mathbb {Q}}}(r)\sim \operatorname{{P}}(r)^{\operatorname... | {
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696c44d6cc8f50018f806f82336d27b5b88c93ad | subsection | 6 | 70 | Introduction | We just briefly check that our results
extend without change
as soon as we have the arity-wise weak-equivalences \operatorname{\mathtt {\Omega }}^*_{\sharp }(\operatorname{{P}})(r)\sim \operatorname{\mathtt {\Omega }}^*(\operatorname{{P}}(r))
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dbf51808fc305066dbf0620fdee2bdb4ce6bdf53 | subsection | 7 | 70 | Introduction | We address this subject in the fourth section of the paper.Finally, we outline the applications of our constructions to the study of the framed little discs operads
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d6dc05cc496da3025696b935601a36b67dc06c08 | subsection | 8 | 70 | The model category of cochain dg-cooperads | We explain the definition of our category of Hopf cochain dg-cooperads with full details in this section.
We also check that this category inherits a model structure.
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fbde8e5e7519bfda1b8040c5134308088a29fe8a | subsection | 9 | 70 | The general definition of a cooperad | Briefly recall that a cooperad \operatorname{{C}} in a symmetric monoidal category \operatorname{\mathcal {C}} consists of a collection of objects \operatorname{{C}}(r)\in \operatorname{\mathcal {C}}, r>0,
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c7c8564765b9480202c11c88a6ba9569c524544d | subsection | 10 | 70 | The general definition of a cooperad | In our subsequent formulas, we also use the identity \operatorname{\mathbb {1}}= \operatorname{\mathbb {Q}} for the unit object
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b7057f16937b97eda987431ebca0215a0b53cf8e | subsection | 11 | 70 | The general definition of a cooperad | We use the notation \operatorname{\mathcal {O}\mathit {p}}_0^c = \operatorname{\mathcal {C}}\operatorname{\mathcal {O}\mathit {p}}_0^c for this category of conilpotent cooperads in \operatorname{\mathcal {C}},
where we assume that the morphisms \phi : \operatorname{{C}}\rightarrow \operatorname{{D}}
preserve all struct... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
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2570b26e5d38ba13c8c9f342ed908b55658ee2ee | subsection | 12 | 70 | The definition of cofree cooperads | In our subsequent constructions, we notably use the conilpotence condition when we define cofree objects in \operatorname{\mathcal {C}}\operatorname{\mathcal {O}\mathit {p}}_0^c.
To be explicit, let \operatorname{\mathcal {S}\mathit {eq}}_{>0}^c = \operatorname{\mathcal {C}}\operatorname{\mathcal {S}\mathit {eq}}_{>0}^... | {
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"Benoit Fresse"
] | [
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34d052c3e1c2cf318f4f113eb630613f86104e80 | subsection | 13 | 70 | The definition of cofree cooperads | Let us mention that we assume by convention r_v>0 for each vertex v in the definition of a tree \operatorname{\underline{\mathsf {T}}},
because our symmetric sequences \operatorname{{N}}= \lbrace \operatorname{{N}}(r),r>0\rbrace
are only defined in arity r>0.
The counit morphism associated to the cofree cooperad \eta ... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
] | 2,018 | en | Mathematics | [
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cac30dcf22111a155d8ef2b102d0d951d48cc13f | subsection | 14 | 70 | The definition of cofree cooperads | The unit morphism of this adjunction \rho : \operatorname{{C}}\rightarrow \operatorname{\mathbb {F}}^c(\bar{\operatorname{{C}}})
is the morphism given by the reduced treewise composition coproducts
of our cooperad \bar{\rho }_{\operatorname{\underline{\mathsf {T}}}}: \bar{\operatorname{{C}}}(r)\rightarrow \operatorname... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
] | 2,018 | en | Mathematics | [
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4b686203d9ae5f3d6cd442c02bc063e34b0bbfe4 | subsection | 15 | 70 | The model category of cooperads in cochain graded dg-modules | The category of cochain graded dg-modules \operatorname{\mathit {dg}}^*\operatorname{\mathcal {M}\mathit {od}} consists of the non-negatively upper graded modules K = \oplus _{n\in \operatorname{\mathbb {N}}} K^n
equipped with a differential \delta : K\rightarrow K
which raises degrees by one. We equip this category \o... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
] | 2,018 | en | Mathematics | [
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4fe67446f0ab5eb1709dbabb443f642dbb8475af | subsection | 16 | 70 | The model category of cooperads in cochain graded dg-modules | We explicitly assume that a morphism of cochain dg-cooperads is:a weak-equivalence \phi : \operatorname{{C}}\xrightarrow{}\operatorname{{D}}
if this morphism defines a weak-equivalence of cochain graded dg-modules \phi : \operatorname{{C}}(r)\xrightarrow{}\operatorname{{D}}(r)
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"Benoit Fresse"
] | [
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69318b32f2b9a82dacde9b7d0712904e922d190e | subsection | 17 | 70 | The model category of cooperads in cochain graded dg-modules | If i: \operatorname{{C}}\hookrightarrow \operatorname{{D}} is also a weak-equivalence, then we can pick such a subcooperad \operatorname{{K}}\subset \operatorname{{D}}
so that the morphism i_{\operatorname{{K}}\cap \operatorname{{C}}}: \operatorname{{K}}\cap \operatorname{{C}}\hookrightarrow \operatorname{{K}}
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"Benoit Fresse"
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77725c4fde61ef0f112d0b4ecf8fab85490e8f82 | subsection | 18 | 70 | The model category of Hopf cochain dg-cooperads | Recall that we call Hopf cochain dg-cooperad the structure defined by a cooperad in the category of commutative cochain dg-algebras,
where a commutative cochain dg-algebra consists of a commutative algebra
in the category of cochain graded dg-modules.
Note that in the case of a Hopf cooperad \operatorname{{A}}, the sec... | {
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"Benoit Fresse"
] | [
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c4d9da3c14012ddabb264ae2cb39df1ee9ee32f7 | subsection | 19 | 70 | The model category of Hopf cochain dg-cooperads | To be explicit, for a cooperad \operatorname{{C}}\in \operatorname{\mathit {dg}}^*\operatorname{\mathcal {O}\mathit {p}}_0^c, we actually have the identity \operatorname{\mathbb {S}}_{\operatorname{\mathcal {O}\mathit {p}}_0^c}(\operatorname{{C}})(1) = \operatorname{\mathbb {S}}(\operatorname{{C}}(1))\otimes _{\operato... | {
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} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
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] | 2,018 | en | Mathematics | [
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5daec35573ac305844c7ed6a58e32557024f9185 | subsection | 20 | 70 | The model category of Hopf cochain dg-cooperads | Furthermore, this category is cofibrantly generated with the morphisms \operatorname{\mathbb {S}}_{\operatorname{\mathcal {O}\mathit {p}}_0^c}(i): \operatorname{\mathbb {S}}_{\operatorname{\mathcal {O}\mathit {p}}_0^c}(\operatorname{{C}})\rightarrow \operatorname{\mathbb {S}}_{\operatorname{\mathcal {O}\mathit {p}}_0^c... | {
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"Benoit Fresse"
] | [
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2e43604afca25e6cd7fa7c9a76c6c94138c64b08 | subsection | 21 | 70 | The model category of Hopf cochain dg-cooperads | This description follows from a straightforward generalization of a result given in
in the category of (Hopf) cochain dg-cooperads which reduce
to the ground field in arity one.To be more explicit, to carry out our construction, we use the operadic cobar-bar adjunction between the category of dg-cooperads
and the cate... | {
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"Benoit Fresse"
] | [
"math.AT"
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91fb5f007a61259c3245aa3620fc418e9151a008 | subsection | 22 | 70 | The model category of Hopf cochain dg-cooperads | (We just need
to consider a filtration by the grading of the bar construction \operatorname{\mathtt {B}}(\operatorname{{C}}),
rather than the filtration by the arity in the proof of the general proposition
which we use to establish our result in this reference.)Let now \operatorname{{P}}= \operatorname{\mathtt {B}}^c(... | {
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"Benoit Fresse"
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6fdbb28ccd744ec6e417e9a416270c4f21124ad4 | subsection | 23 | 70 | The model category of Hopf cochain dg-cooperads | Let \operatorname{{P}}^{\bullet } = \operatorname{\mathtt {B}}^c(\operatorname{{C}}^{\bullet }) denote the image of this cosimplicial cochain dg-cooperad
under the operadic cobar construction \operatorname{\mathtt {B}}^c(-).The object \operatorname{\mathtt {B}}(\operatorname{{P}}^{\bullet })^{\Delta ^{\bullet }} = \ope... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
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e41036e08c167a65466a3656a4b82529bebc0ce9 | subsection | 24 | 70 | The model category of Hopf cochain dg-cooperads | For such an object \operatorname{{K}}^{\bullet } = \operatorname{\mathtt {B}}\operatorname{\mathtt {B}}^c(\operatorname{{C}}^{\bullet }), we have a chain of natural weak-equivalences of cochain dg-cooperads
\operatorname{\mathtt {Tot}}(\operatorname{\mathtt {B}}\operatorname{\mathtt {B}}^c(\operatorname{{C}}^{\bullet ... | {
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"Benoit Fresse"
] | [
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fd880fdd6e69e2bcb1df2939a55b63fdeb10e120 | subsection | 25 | 70 | The operadic upgrading of the Sullivan model functor | We now explain the definition of our adjunction \operatorname{\mathtt {G}}: \operatorname{\mathit {dg}}^*\operatorname{\mathcal {H}\mathit {opf}}\operatorname{\mathcal {O}\mathit {p}}_0^c\rightleftarrows \operatorname{\mathit {s}\mathcal {S}\mathit {et}}\operatorname{\mathcal {O}\mathit {p}}_{\varnothing }^{op} :\opera... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
] | 2,018 | en | Mathematics | [
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bc5929f96025759a3576e3122b27175cd2a000c1 | subsection | 26 | 70 | The operadic enhancement of the Sullivan cochain dg-algebra functor | Recall that the functor \operatorname{\mathtt {G}}: \operatorname{\mathit {dg}}^*\operatorname{\mathcal {C}\mathit {om}}\rightarrow \operatorname{\mathit {s}\mathcal {S}\mathit {et}}^{op} is defined by \operatorname{\mathtt {G}}(A) = \operatorname{\mathtt {Mor}}_{\operatorname{\mathit {dg}}^*\operatorname{\mathcal {C}\... | {
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} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
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6975e5c48ad257aa75187c6bc53eda980ba4f402 | subsection | 27 | 70 | The operadic enhancement of the Sullivan cochain dg-algebra functor | This result implies that the collection \operatorname{\mathtt {G}}(\operatorname{{A}})(r) = \operatorname{\mathtt {Mor}}_{\operatorname{\mathit {dg}}^*\operatorname{\mathcal {C}\mathit {om}}}(\operatorname{{A}}(r),\operatorname{\mathtt {\Omega }}^*(\Delta ^{\bullet }))
associated to a Hopf cochain dg-cooperad \operator... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
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d77821af04440aaf694745b0835a9f64961a6563 | subsection | 28 | 70 | The operadic enhancement of the Sullivan cochain dg-algebra functor | In short, we first set \operatorname{\mathtt {\Omega }}^*_{\sharp }(\operatorname{\mathbb {F}}(\operatorname{{M}})) = \operatorname{\mathbb {F}}^c(\operatorname{\mathtt {\Omega }}^*(\operatorname{{M}})) for a free operad \operatorname{{P}}= \operatorname{\mathbb {F}}(\operatorname{{M}})
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866c7ef24e33f67d1f1751a01b5324173bc1dc68 | subsection | 29 | 70 | The operadic enhancement of the Sullivan cochain dg-algebra functor | Then we easily check that:Proposition 2.11
The functors \operatorname{\mathtt {G}}: \operatorname{\mathit {dg}}^*\operatorname{\mathcal {H}\mathit {opf}}\operatorname{\mathcal {O}\mathit {p}}_0^c\rightleftarrows \operatorname{\mathit {s}\mathcal {S}\mathit {et}}\operatorname{\mathcal {O}\mathit {p}}_{\varnothing }^{op... | {
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"Benoit Fresse"
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27136a4b9cc93e781bbd9a13cabcc7ea9545643c | subsection | 30 | 70 | The operadic enhancement of the Sullivan cochain dg-algebra functor | We just use that the (acyclic) fibrations of the category of operads in simplicial sets are precisely the operad morphisms
which form an (acyclic) fibration in the category of simplicial sets
to deduce from this result that our functor \operatorname{\mathtt {G}}: \operatorname{\mathit {dg}}^*\operatorname{\mathcal {H}\... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
] | 2,018 | en | Mathematics | [
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9b5404c49e95e87c151f13975ad7597586f8d315 | subsection | 31 | 70 | The operadic enhancement of the Sullivan cochain dg-algebra functor | We assume that the space \operatorname{{P}}(1) is connected
and that the spaces \operatorname{{P}}(r) have a homology with rational coefficients \operatorname{\mathtt {H}}_*(\operatorname{{P}}(r)) = \operatorname{\mathtt {H}}_*(\operatorname{{P}}(r),\operatorname{\mathbb {Q}})
which form a module of finite dimension ov... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
] | 2,018 | en | Mathematics | [
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d729ebe61da96723dae7e4fd01f9a86b370de265 | subsection | 32 | 70 | The operadic James construction | We consider the category of under-objects \operatorname{{I}}/\operatorname{\mathit {s}\mathcal {S}\mathit {et}}\operatorname{\mathcal {S}\mathit {eq}}_{>0} in the category of symmetric sequences in simplicial sets \operatorname{\mathit {s}\mathcal {S}\mathit {et}}\operatorname{\mathcal {S}\mathit {eq}}_{>0}
where \oper... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
] | 2,018 | en | Mathematics | [
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245a66e453decf48dfb004428e8c02733a74b64b | subsection | 33 | 70 | The reduced cotriple resolution of operads | We easily see that the mapping \operatorname{\mathbb {F}}_*: \operatorname{{M}}\mapsto \operatorname{\mathbb {F}}_*(\operatorname{{M}})
defines a left adjoint of the obvious functor \omega _*: \operatorname{\mathit {s}\mathcal {S}\mathit {et}}\operatorname{\mathcal {O}\mathit {p}}_{\varnothing }\rightarrow \operatornam... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
] | 2,018 | en | Mathematics | [
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d7e16cec9641312d6b09bdea0e8780a761ca132c | subsection | 34 | 70 | The reduced cotriple resolution of operads | The face operators d_i: \operatorname{\mathtt {Res}}_*(\operatorname{{P}})_n\rightarrow \operatorname{\mathtt {Res}}_*(\operatorname{{P}})_{n-1}
are defined by applying an adjunction augmentation \lambda : \operatorname{\mathbb {F}}_*\omega _*\rightarrow \operatorname{\mathit {Id}} on the i+1st factor \operatorname{\ma... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
] | 2,018 | en | Mathematics | [
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0379b305108f8ce83183c5b215bff781a48bb9ca | subsection | 35 | 70 | The reduced cotriple resolution of operads | Furthermore, the augmentation \operatorname{\mathtt {Res}}_*(\operatorname{{P}})_{\bullet }\rightarrow \operatorname{{P}} induces a weak-equivalence |\operatorname{\mathtt {Res}}_*(\operatorname{{P}})_{\bullet }|\xrightarrow{}\operatorname{{P}}
when we pass to the geometric realization in \operatorname{\mathit {s}\math... | {
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"Benoit Fresse"
] | [
"math.AT"
] | 2,018 | en | Mathematics | [
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73f9a7c608fb227c15a1c1ec7f1ecd57361ae199 | subsection | 36 | 70 | The reduced cotriple resolution of operads | We rely on the following observation:Proposition 2.16
For the operadic James construction \operatorname{{P}}= \operatorname{\mathbb {F}}_*(\operatorname{{M}}), we have an identity:\operatorname{\mathtt {\Omega }}_{\sharp }^*(\operatorname{\mathbb {F}}_*(\operatorname{{M}})) = \operatorname{\mathbb {F}}^c(\overline{\op... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
] | 2,018 | en | Mathematics | [
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3defc01790ec01d41c3acbf61dc4cfb6c1374ea6 | subsection | 37 | 70 | The reduced cotriple resolution of operads | In fact, we can identify the collection \operatorname{{I}}^c with the final object in the category of Hopf cochain dg-cooperads,
and this relation \operatorname{\mathtt {\Omega }}^*_{\sharp }(\operatorname{{I}}) = \operatorname{{I}}^c also follows from the observation that the right adjoint functor \operatorname{\matht... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
] | 2,018 | en | Mathematics | [
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32baf7d3d3ce0d6a68398d2d306a14f0307649af | subsection | 38 | 70 | The reduced cotriple resolution of operads | The result of the lemma just follows from the observation that the cofree cooperad functor carries the obvious pullback diagram{ \overline{\operatorname{\mathtt {\Omega }}^*(\operatorname{{M}})}@{.>}[d]@{.>}[r] & 0[d] \\
\operatorname{\mathtt {\Omega }}^*(\operatorname{{M}})[r] & \operatorname{\mathtt {\Omega }}^*(\ope... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
] | 2,018 | en | Mathematics | [
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b4cd2e4064bafb0b0a9cc039eb335e3d5c4a7efd | subsection | 39 | 70 | The reduced cotriple resolution of operads | For the free operad \operatorname{\mathbb {F}}(\operatorname{{M}}) associated to a symmetric collection in simplicial sets \operatorname{{M}}\in \operatorname{\mathit {s}\mathcal {S}\mathit {et}}\operatorname{\mathcal {S}\mathit {eq}}_{>0},
we dually have \operatorname{\mathbb {F}}(\operatorname{{M}}) = \coprod _{[\ope... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
] | 2,018 | en | Mathematics | [
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b8ffa882104bc3c98902decbf3fe6e8bcd5dea1d | subsection | 40 | 70 | The reduced cotriple resolution of operads | We easily check that the image of such a tensor \alpha = \bigotimes _v\alpha _v\in \operatorname{\mathbb {F}}^c_{\operatorname{\underline{\mathsf {T}}}}(\overline{\operatorname{\mathtt {\Omega }}^*(\operatorname{{M}})})
under our comparison morphism \chi : \operatorname{\mathtt {\Omega }}^*_{\sharp }(\operatorname{\mat... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
] | 2,018 | en | Mathematics | [
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eba5ec1b94b28287f8d86c2e2706de8317042347 | subsection | 41 | 70 | The reduced cotriple resolution of operads | We have a cofiber sequence of simplicial sets{ \operatorname{\mathbb {F}}^{\le m-1}_*(\operatorname{{M}})(r)[r] & \operatorname{\mathbb {F}}^{\le m}_*(\operatorname{{M}})(r)[r] & \bigvee _{\sharp V(\operatorname{\underline{\mathsf {T}}}) = m}\operatorname{\mathbb {F}}_{\operatorname{\underline{\mathsf {T}}}}^{\wedge }(... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
] | 2,018 | en | Mathematics | [
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eeb40215323870a3e512e2b1b08d02a87e91e430 | subsection | 42 | 70 | The reduced cotriple resolution of operads | We see that our comparison morphism arises as the limit
of a tower of comparison maps \chi : \operatorname{\mathbb {F}}^c_{\le m}(\overline{\operatorname{\mathtt {\Omega }}^*(\operatorname{{M}})})(r)\rightarrow \operatorname{\mathtt {\Omega }}^*(\operatorname{\mathbb {F}}^{\le m}_*(\operatorname{{M}})(r))
which fit in ... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
] | 2,018 | en | Mathematics | [
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4d2da9914bf15e3d9788f62ab98e153ae4320f44 | subsection | 43 | 70 | The reduced cotriple resolution of operads | We obtain by induction that the medium vertical map defines a weak-equivalence as well for each m\ge 0.Then the assumption that the simplicial set \operatorname{{M}}(1) is connected
implies that the map \operatorname{\mathtt {\Omega }}^*(\operatorname{\mathbb {F}}_*^{\le m}(\operatorname{{M}})(r))\rightarrow \operatorn... | {
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"Benoit Fresse"
] | [
"math.AT"
] | 2,018 | en | Mathematics | [
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521db0afe779a6b3f4138101b6f87edf0fea0fc8 | subsection | 44 | 70 | The reduced cotriple resolution of operads | By Quillen adjunction, we can also identify the right-hand side
of this formula with the totalization of the cosimplicial object \operatorname{\mathtt {\Omega }}^*_{\sharp }(\operatorname{{R}}_{\bullet })
in the category of Hopf cochain dg-cooperads, and hence, in the category of cochain dg-cooperads
since the forgetfu... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
] | 2,018 | en | Mathematics | [
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2984a76ee70fc6b6b98e12b22ab2db554be6e226 | subsection | 45 | 70 | The reduced cotriple resolution of operads | To be explicit, we check that our morphism (1) fits in the following commutative diagram of weak-equivalences
when we forget about Hopf structures and we work in the category of cochain dg-cooperads:{ \operatorname{\mathtt {\Omega }}_{\sharp }^*(\operatorname{{P}})[r]^-{\sim }[dd]_-{\sim } &
\operatorname{\mathtt {\Ome... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
] | 2,018 | en | Mathematics | [
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d77b6f94800d4d59734e5be98654d01d7bbff008 | subsection | 46 | 70 | The reduced cotriple resolution of operads | The weak-equivalences (4-5) are given by a natural comparison zigzag
of totalizations, and the weak-equivalence (6) is given by the result of Theorem REF .The result of Proposition REF
implies that the vertical comparison morphism (3)
on the right-hand side of our diagram (REF )
is a weak-equivalence too, because the ... | {
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"Benoit Fresse"
] | [
"math.AT"
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4feff9a956141b9c026bc3bb24ee6bf7dbc50f32 | subsection | 47 | 70 | The reduced cotriple resolution of operads | We have a natural one-to-one correspondence between the morphisms of Hopf cochain dg-cooperads\phi _{\sharp }: \operatorname{{A}}\rightarrow \operatorname{\mathtt {\Omega }}_{\sharp }^*(\operatorname{{P}})and the collections of morphisms of unitary commutative cochain dg-algebras\phi : \operatorname{{A}}(r)\rightarrow ... | {
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"Benoit Fresse"
] | [
"math.AT"
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f1483ad0d3e6898e0c288acd518bd3568079f141 | subsection | 48 | 70 | The reduced cotriple resolution of operads | Then we use the adjunction relation \operatorname{\mathtt {G}}: \operatorname{\mathit {dg}}^*\operatorname{\mathcal {C}\mathit {om}}\rightleftarrows \operatorname{\mathit {s}\mathcal {S}\mathit {et}}^{op} :\operatorname{\mathtt {\Omega }}^*
to associate morphisms of commutative cochain dg-algebras \phi : \operatorname{... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
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46eba89f67975698a26f8d202f25006098640643 | subsection | 49 | 70 | The rational homotopy theory of operads | We explain the consequences of the results of the previous section for the study of the rational homotopy of operads in this section.
We actually get the same results as in in the context of operads
that reduce to a one-point set in arity one.
We therefore only give a brief overview of the main statements.Recall that ... | {
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"Benoit Fresse"
] | [
"math.AT"
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ca3321de3ee32d93a95611d12813a958c4c4cf36 | subsection | 50 | 70 | The rational homotopy theory of operads | We have the following result:Theorem 3.19
We assume that the operad \operatorname{{P}} consists of connected simplicial sets \operatorname{{P}}(r)
whose homology with rational coefficients \operatorname{\mathtt {H}}_*(\operatorname{{P}}(r)) = \operatorname{\mathtt {H}}_*(\operatorname{{P}}(r),\operatorname{\mathbb {Q}... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
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cd7d9b26f609f249d0cff37a8232036538b6ca74 | subsection | 51 | 70 | The rational homotopy theory of operads | The conclusion follows.For our purpose, we also record the following immediate follow-up of our constructions:Theorem 3.20
Let \operatorname{{P}},\operatorname{{Q}}\in \operatorname{\mathit {s}\mathcal {S}\mathit {et}}\operatorname{\mathcal {O}\mathit {p}}_{\varnothing }. We have a weak-equivalence of simplicial sets:... | {
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b631dcc615cf0381faf92a765e6b1e76b459ff4b | subsection | 52 | 70 | The extension to unitary operads | Recall that we use the notation \Lambda for the category which has the finite ordinals \operatorname{\underline{\mathsf {r}}}= \lbrace 1<\dots ,r\rbrace
and all injective maps (not necessarily monotoneous) between such ordinals as morphisms.
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b0ed990bc701e9f995740296f4263c8702c04967 | subsection | 53 | 70 | The extension to unitary operads | The augmentation map \epsilon : \operatorname{{P}}(r)\rightarrow \operatorname{\mathit {pt}} (which is just trivial in our context)
can be identified with the composition operation \epsilon (p) = p(*,\dots ,*)
where we put the arity zero element *\in \operatorname{{P}}_+(0)
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94bee113b9c11e9d38658d7903f9e9d0dbf32d84 | subsection | 54 | 70 | The model category of cochain dg- | For our purpose, a cochain dg-\Lambda -cooperad consists of a (conilpotent) cooperad in cochain graded dg-modules \operatorname{{C}},
in the sense of §REF ,
together with corestriction operators u_*: \operatorname{{C}}(k)\rightarrow \operatorname{{C}}(l),
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a6be0a3629afd0bcce7ebaf5e6664dc1b3cf4f6c | subsection | 55 | 70 | The model category of cochain dg- | Let us mention that we use an analogue of this category of \Lambda -cooperads
in the category of general (unbounded) dg-modules
as an auxiliary category in the paper .We have an obvious forgetful functor \omega : \operatorname{{Com}}^c/\operatorname{\mathit {dg}}^*\Lambda \operatorname{\mathcal {O}\mathit {p}}_0^c\righ... | {
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b47c1c17cad5c6edbe68d5c8d2eda79ee0ffad45 | subsection | 56 | 70 | The model category of cochain dg- | (In particular, we still get that a morphism of cochain dg-\Lambda -cooperads
is a weak-equivalence \phi : \operatorname{{C}}\xrightarrow{}\operatorname{{D}} if this morphism induces an isomorphism in cohomology.)
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b8e9210a2a577121d1f7e1e7ff9c4798e14fac4e | subsection | 57 | 70 | The model category of Hopf cochain dg- | We define our category of Hopf cochain dg-\Lambda -cooperads by an obvious extension,
in the category of commutative cochain dg-coalgebras,
of our notion of a cochain dg-\Lambda -cooperad. Thus, we assume that a Hopf cochain dg-\Lambda -cooperad \operatorname{{A}}
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equ... | {
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b8078564ff6f83beea86787a3041d5b189e0b4e7 | subsection | 58 | 70 | The model category of Hopf cochain dg- | We also use an analogue of this category of Hopf \Lambda -cooperads
in the category of general (unbounded) dg-modules
in the paper .We have a commutative square of forgetful and adjoint functors that relate the category of Hopf cochain dg-\Lambda -cooperads \operatorname{\mathit {dg}}^*\operatorname{\mathcal {H}\mathit... | {
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50f402c54599fa7125a60e638b1f1e6514693c46 | subsection | 59 | 70 | The model category of Hopf cochain dg- | We already explained that the functor \operatorname{{Com}}^c/\Lambda \otimes _{\Sigma }-: \operatorname{\mathcal {C}\mathit {om}}^c/\operatorname{\mathit {dg}}^*\operatorname{\mathcal {O}\mathit {p}}_0^c\rightarrow \operatorname{\mathcal {C}\mathit {om}}^c/\operatorname{\mathit {dg}}^*\Lambda \operatorname{\mathcal {O}... | {
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439bab08e94b8951ad0356925a776cf77c486f37 | subsection | 60 | 70 | The model category of Hopf cochain dg- | We just check that this Hopf cooperad \operatorname{{Com}}^c/\operatorname{\mathbb {S}}(\operatorname{{C}})(r) = \operatorname{\mathbb {S}}(\operatorname{{C}}(r))\otimes _{\operatorname{\mathbb {S}}(\operatorname{\mathbb {Q}})}\operatorname{\mathbb {Q}}
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506ab19edea61ff3d53a6e6cb6a4f1bdb317f12e | subsection | 61 | 70 | The model category of Hopf cochain dg- | The proof of the validity of the definition of this cofibrantly generated model structure
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04634c4b591ce7c10a47ce297ef25ad8fbfe1a96 | subsection | 62 | 70 | The model category of Hopf cochain dg- | We accordingly get that the functor \operatorname{\mathtt {G}}: \operatorname{\mathit {dg}}^*\operatorname{\mathcal {H}\mathit {opf}}\operatorname{\mathcal {O}\mathit {p}}_0^c\rightarrow \operatorname{\mathit {s}\mathcal {S}\mathit {et}}\operatorname{\mathcal {O}\mathit {p}}_{\varnothing }^{op}
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e90da0f2aea6852fc0424feb48168c12e7533661 | subsection | 63 | 70 | The model category of Hopf cochain dg- | We have in particular \operatorname{\mathtt {\Omega }}^*_{\sharp }(\operatorname{\mathbb {F}}(\operatorname{{M}})) = \operatorname{\mathbb {F}}^c(\operatorname{\mathtt {\Omega }}^*(\operatorname{{M}}))
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eafc6794de12c443fc658ef2805091e929435337 | subsection | 64 | 70 | The model category of Hopf cochain dg- | We have the following observation:Proposition 4.24
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502decb752cabd9439c031f31a95933006ce9152 | subsection | 65 | 70 | The model category of Hopf cochain dg- | Note simply that the observation that the functor \operatorname{\mathtt {\Omega }}^*_{\sharp }: \operatorname{\mathit {s}\mathcal {S}\mathit {et}}\Lambda \operatorname{\mathcal {O}\mathit {p}}_{\varnothing }^{op}\rightarrow \operatorname{\mathit {dg}}^*\operatorname{\mathcal {H}\mathit {opf}}\Lambda \operatorname{\math... | {
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91b5dfe9856262bfd82bb81198fcfb59046dc47b | subsection | 66 | 70 | The model category of Hopf cochain dg- | In particular, if we assume that \operatorname{{P}} is a cofibrant \Lambda -operad in simplicial sets
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02c6dda929eb3b073f31c5ef462d56d947f65386 | subsection | 67 | 70 | The model category of Hopf cochain dg- | Note simply that the derived mapping spaces of objects \operatorname{{P}}_+,\operatorname{{Q}}_+\in \operatorname{\mathit {s}\mathcal {S}\mathit {et}}\operatorname{\mathcal {O}\mathit {p}}_*
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9d7f894fa18cdba8038d4c68f8a0302bd48d59cd | subsection | 68 | 70 | The applications to the framed little discs operads | Recall that the framed little n-discs operad \operatorname{{D}}_n^{fr}
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617536abdb96f5b5df8221c205c80ab57c416d36 | subsection | 69 | 70 | The applications to the framed little discs operads | We conclude from this result that the operad <\operatorname{\mathtt {H}}^*(\operatorname{{D}}_n^{fr})> = |\operatorname{\mathtt {L}}\operatorname{\mathtt {G}}(\operatorname{\mathtt {H}}^*(\operatorname{{D}}_n^{fr}))|
where we consider the geometric realization functor |-| and the left adjoint functor \operatorname{\mat... | {
"cite_spans": []
} | 10.1515/gmj-2018-0061 | 1805.00530 | The extended rational homotopy theory of operads | [
"Benoit Fresse"
] | [
"math.AT"
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a79221921a048c262a768688942660d99710d0e6 | abstract | 0 | 5 | Abstract | Accessible epidemiological data are of great value for emergency preparedness
and response, understanding disease progression through a population, and
building statistical and mechanistic disease models that enable forecasting.
The status quo, however, renders acquiring and using such data difficult in
practice. In ma... | {
"cite_spans": []
} | 10.3389/fpubh.2018.00336 | 1805.00445 | Epidemiological data challenges: planning for a more robust future
through data standards | [
"Geoffrey Fairchild",
"Byron Tasseff",
"Hari Khalsa",
"Nicholas Generous",
"Ashlynn R. Daughton",
"Nileena Velappan",
"Reid Priedhorsky",
"Alina Deshpande"
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3908607da6012c3c0d47550a74bcab82f1366d17 | subsection | 1 | 5 | Introduction | At the heart of disease surveillance and modeling are epidemiological data. These data are generally presented as a time series of cases, T, for a geographic region, G, and for a demographic, D. The type of cases presented may vary depending on the context. For example, T may be a time series of confirmed or suspected ... | {
"cite_spans": []
} | 10.3389/fpubh.2018.00336 | 1805.00445 | Epidemiological data challenges: planning for a more robust future
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"Geoffrey Fairchild",
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"Nicholas Generous",
"Ashlynn R. Daughton",
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e0890b7e20244fcf8d3c8f51f923224c72d66ffc | subsection | 2 | 5 | Introduction | Compounding these issues, formats can change over time (e.g., renaming or reordering spreadsheet columns). More broadly, these challenges are closely tied to schema, data model, and vocabulary standardization.Finally, there are differences among institutions in their reporting habits; even within a single institution, ... | {
"cite_spans": []
} | 10.3389/fpubh.2018.00336 | 1805.00445 | Epidemiological data challenges: planning for a more robust future
through data standards | [
"Geoffrey Fairchild",
"Byron Tasseff",
"Hari Khalsa",
"Nicholas Generous",
"Ashlynn R. Daughton",
"Nileena Velappan",
"Reid Priedhorsky",
"Alina Deshpande"
] | [
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90dd39b798b5e53f974d208d97ae02494aafb2af | subsection | 3 | 5 | Interface challenges | The interface is the mechanism by which data are presented to a user for consumption.Epidemiological data repositories implementing current best practices provide an interactive web-based searching and filtering interface that enables users to easily export desired data in a variety of formats. These are generally acco... | {
"cite_spans": []
} | 10.3389/fpubh.2018.00336 | 1805.00445 | Epidemiological data challenges: planning for a more robust future
through data standards | [
"Geoffrey Fairchild",
"Byron Tasseff",
"Hari Khalsa",
"Nicholas Generous",
"Ashlynn R. Daughton",
"Nileena Velappan",
"Reid Priedhorsky",
"Alina Deshpande"
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"cs.CY",
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0.... |
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