chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
14,053 | lean_file_chunk | 63dbae2ff78ff07fafed393ab353ede15c0f98d519ee9eab0fa5482a0cf5f248 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.Algebra.Group.Hom.Defs
public import Mathlib.GroupTheory.Congruence.Defs
/-!
# Congruence relations and homomorphisms
This file ... |
23,965 | lean_file_chunk | d62a679a7d1a80399cfeb578113691babca19ff56bcdefa8b68d998e5b2672a8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Antoine Chambert-Loir
-/
module
public import Mathlib.Data.Fintype.Units
public import Mathlib.GroupTheory.IndexNormal
public import Mathlib.GroupTheory.Perm.ConjAct
p... |
558 | lean_file_chunk | 70135fc2a2eeb25cf814cb305cd62df2d410faefaad9139a0fc0fe0fccad0928 | lean_source_file | pkg_mathlib_source_file_chunks | rcases G.index.eq_zero_or_pos with h | h
· exact (index_ne_zero_of_finite h).elim
rcases (Nat.succ_le_iff.mpr h).eq_or_lt' with h | h
· exact index_eq_one.mp h ▸ le_top
rw [eq_alternatingGroup_of_index_eq_two (hG.antisymm h)]
end Equiv.Perm
/-- The alternating group is a characteristic subgroup of the permuta... |
10,911 | lean_file_chunk | 97103efbd03039cc2cca96f6eae2e81089bfc257f69230d2cc00c8fdabae2c2f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Shing Tak Lam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shing Tak Lam
-/
module
public import Mathlib.Data.Finite.Sum
public import Mathlib.Data.ZMod.Basic
public import Mathlib.GroupTheory.Exponent
public import Mathlib.GroupTheory.GroupAc... |
23,996 | lean_file_chunk | 862f1961a51e4396d876515fa80297ff3d6700b2dd17b22935b2f19da7146ee0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
module
public import Mathlib.Algebra.Group.TypeTags.Finite
public import Mathlib.Algebra.Order.Hom.TypeTags
public import Mathlib.Data.Nat.Totient
public import Math... |
11,699 | lean_file_chunk | 0cf231adddb8440dcdc7349c408e160e5d6a867d262cd81a5eb6abf41176f9b0 | lean_source_file | pkg_mathlib_source_file_chunks | simp
/-- An infinite cyclic additive group is isomorphic to `ℤ`. -/
noncomputable
abbrev intCyclicAddEquiv [AddGroup G] [IsAddCyclic G] : ℤ ≃+ G :=
intEquivOfZMultiplesEqTop _ (isAddCyclic_iff_exists_zmultiples_eq_top.mp ‹_›).choose_spec
end Infinite
variable (G) in
/-- The automorphism group of a cyclic group is ... |
15,459 | lean_file_chunk | d0fb7994ea7a06bba9eca9baf8a5957861e8aa7cee595d1391c8cf82e6451837 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
module
public import Mathlib.FieldTheory.Finite.Basic
public import Mathlib.GroupTheory.Abelianization.Finite
public import Mathlib.GroupTheory.Nilpotent
public im... |
8,557 | lean_file_chunk | 4d01311a078024b372df5f5c0c5784205097dbc707239c7714ee78d2d48f77f9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
module
public import Mathlib.GroupTheory.SpecificGroups.Cyclic
public import Mathlib.GroupTheory.SpecificGroups.Dihedral
/-!
# Quaternion Groups
We define ... |
6,842 | lean_file_chunk | ae65c890efaa94e0568c4529e89ccd9a22f6bc5a0e034b33db079572a261c801 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Newell Jensen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Newell Jensen
-/
module
public import Mathlib.GroupTheory.SpecificGroups.Cyclic
/-!
# Klein Four Group
The Klein (Vierergruppe) four-group is a non-cyclic abelian group with four ele... |
5,063 | lean_file_chunk | 6a1902c9f3dbccd7bcc14a01f6a2ca14d221b179cdff4c32dfc9358ef89adb43 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer, Kevin Klinge
-/
module
public import Mathlib.Algebra.Group.Submonoid.Defs
/-!
# (Left) Ore sets
This defines left Ore sets on arbitrary monoids.
## References
... |
23,980 | lean_file_chunk | cefc7fa21732b293a7fa74201cd8e777b9ac6e2ba6e39cc668c4c7ed010594d6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer, Kevin Klinge, Andrew Yang
-/
module
public import Mathlib.GroupTheory.OreLocalization.OreSet
public import Mathlib.Tactic.Common
public import Mathlib.Algebra.Grou... |
2,568 | lean_file_chunk | 6209638258c7b0a9c91883044437f0b315d0fc221ed74ade19f8b12e20dcc0ae | lean_source_file | pkg_mathlib_source_file_chunks | rw [← smul_one_oreDiv_one_smul, ← smul_one_oreDiv_one_smul, ← smul_one_oreDiv_one_smul,
← mul_smul, mul_div_one]
simp only [smul_mul_assoc, smul_assoc, one_mul]
@[to_additive]
instance [SMulCommClass R R' M] : SMulCommClass R R' X[S⁻¹] where
smul_comm r m x := by
rw [← smul_one_smul m, ← smul_assoc, sm... |
3,975 | lean_file_chunk | a370046f981ff8a551fdec7b6ef368d28d27a1d39e6d528ea05266144a2e6f72 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
module
public import Mathlib.Data.Fintype.Pigeonhole
public import Mathlib.GroupTheory.OreLocalization.Basic
public import Mathlib.SetTheory.Cardinal.Arithmetic
/-!
# Cardinality ... |
1,338 | lean_file_chunk | daeedd47b7f478dc0aa8bcd072ec8c823c06b103cc56c770cb269a7d2d69d4d3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yaël Dillies, Patrick Luo. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Patrick Luo
-/
module
public import Mathlib.GroupTheory.Finiteness
public import Mathlib.GroupTheory.MonoidLocalization.GrothendieckGroup
/-!
# Localization ... |
6,196 | lean_file_chunk | 87fc24ab014a05cd9399d141de6177211b5feb7ca2619d8f29b8b21633e76228 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.Algebra.Group.Submonoid.Membership
public import Mathlib.GroupTheory.MonoidLocalization.Maps
/-!
# Localizing commutative monoids... |
3,526 | lean_file_chunk | 868be018874d2cfc4afa22c47e413e09593380816947e69bc3f6aa831e0463ad | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Alex J. Best, Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex J. Best, Yaël Dillies
-/
module
public import Mathlib.GroupTheory.MonoidLocalization.Maps
/-!
# Grothendieck group
The Grothendieck group of a commutative monoid `M... |
1,738 | lean_file_chunk | a7b7ae1c482630d6f6b316f5b1be6763dc2bd0e68e26229dc988c9cd1709a52e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
module
public import Mathlib.Algebra.Group.Pi.Units
public import Mathlib.Data.Fintype.Basic
public import Mathlib.GroupTheory.MonoidLocalization.Basic
/-!
# Lemmas about loc... |
23,995 | lean_file_chunk | 2cd4ee4a484aee9bb6059b5d9f7be79810b31a9a10124ebe8a9916f66c9a0ef5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.GroupTheory.MonoidLocalization.Basic
/-!
# Mapping properties of monoid localizations
Given an `S`-localization map `f : M →* N`... |
6,256 | lean_file_chunk | 4a5647da16861088fc1b26cc774866a5194071b6de463cf9fe5e100ddad07fee | lean_source_file | pkg_mathlib_source_file_chunks | /-- Given `AddCommMonoid`s `M, P` and `AddSubmonoid`s `S ⊆ M, T ⊆ P`, if `f : M →* N` is a
Localization map for `S` and `k : P ≃+ M` is an isomorphism of `AddCommMonoid`s such that
`k(T) = S`, `f ∘ k` is a Localization map for `T`. -/]
def ofMulEquivOfDom {k : P ≃* M} (H : T.map k.toMonoidHom = S) : LocalizationMap T N... |
4,524 | lean_file_chunk | 5012567b20ccf57e7de93aa8fd9274b4c84877c755e9bbc327a66c7f60639088 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.Algebra.Order.Monoid.Defs
public import Mathlib.GroupTheory.MonoidLocalization.Basic
/-!
# Ordered structures on localizations of... |
6,096 | lean_file_chunk | 6bc77ea87c97182f566a584169686b46f018fedf0994f4c4b7eacb9ccae3a88e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.Algebra.GroupWithZero.Hom
public import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
public import Mathlib.Algebra.GroupWithZero.... |
23,991 | lean_file_chunk | cbe1c19d5a7a98e58a6660871c72205313ecad742f650b9ddf6a7314b8a7a8c0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Basic
public import Mathlib.Algebra.Group.Submonoid.Operations
public import Mathlib.Algebra.Reg... |
14,649 | lean_file_chunk | 5a4172725189d2503f4eceaf84288e19974ded0554fcc98de2f9a842df5a6d7f | lean_source_file | pkg_mathlib_source_file_chunks | f x = f y := by
rw [map_mul, map_mul] at h
let ⟨u, hu⟩ := f.map_units c
rw [← hu] at h
exact (Units.mul_right_inj u).1 h
@[to_additive]
theorem map_left_cancel {x y} {c : S} (h : f (x * c) = f (y * c)) :
f x = f y :=
f.map_right_cancel (c := c) <| by rw [mul_comm _ x, mul_comm _ y, h]
/-- Given a locali... |
637 | lean_file_chunk | 764d9372ed1578ab1f5b8c98291709621b9acaed9c9450b52c276ed3d90395e5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
module
public import Mathlib.GroupTheory.MonoidLocalization.Basic
public import Mathlib.GroupTheory.OreLocalization.Cardinality
/-!
# Cardinality of localizations of commutative m... |
1,498 | lean_file_chunk | 71c9edb55feea799d8f9abc5a933656bfb6a91594d7913cdbc8b29e6878af657 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yaël Dillies, Michał Mrugała. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Michał Mrugała
-/
module
public import Mathlib.GroupTheory.MonoidLocalization.Maps
/-!
# Submonoid of pairs with quotient in a submonoid
This file define... |
8,902 | lean_file_chunk | 890555445c2044eadfe39748174fee3a09a61aaca90ef37a9d78cf31f603b76a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yudai Yamazaki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yudai Yamazaki
-/
module
public import Mathlib.GroupTheory.GroupExtension.Defs
public import Mathlib.GroupTheory.SemidirectProduct
public import Mathlib.GroupTheory.QuotientGroup.Basi... |
12,504 | lean_file_chunk | 006d4df38fcb13f1eb202346775a42610b0478644d3d41c4e77a9e02a3157e44 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yudai Yamazaki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yudai Yamazaki
-/
module
public import Mathlib.GroupTheory.GroupAction.ConjAct
public import Mathlib.GroupTheory.SemidirectProduct
/-!
# Group Extensions
This file defines extension... |
10,180 | lean_file_chunk | 81899c73d937e78a4e8b96c6fdc97a77b7a96620f907c4613f91de8e13da7157 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn, Eric Wieser, Joachim Breitner
-/
module
public import Mathlib.GroupTheory.FreeGroup.Basic
/-!
# Free groups structures on arbitrary types
This file defines the notion of fre... |
23,921 | lean_file_chunk | 43234a786bb598d72278f41bc4fb21bc2e23d0cddca78225c724ec4aebb18b91 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
module
public import Mathlib.Algebra.Group.Pi.Basic
public import Mathlib.Algebra.Group.Subgroup.Ker
public import Mathlib.Data.List.Chain
public import Mathlib.Algebra.Group.... |
15,625 | lean_file_chunk | 2d122538f42e2cc6f92aa361ea03daf5032cf1e696a3a6212b9b16e521d1d474 | lean_source_file | pkg_mathlib_source_file_chunks | /-- Two homomorphisms out of a free group are equal if they are equal on generators.
See note [partially-applied ext lemmas]. -/
@[to_additive (attr := ext) /-- Two homomorphisms out of a free additive group are equal if they are
equal on generators. See note [partially-applied ext lemmas]. -/]
lemma ext_hom {M : Ty... |
10,212 | lean_file_chunk | 08b3ca0781b9f0bdd8b34d821e2a3f9017154165c43d5ac446e685c823fd8b66 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Bernhard Reinke. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amir Livne Bar-on, Bernhard Reinke
-/
module
public import Mathlib.Data.List.Induction
public import Mathlib.GroupTheory.FreeGroup.Basic
public import Mathlib.GroupTheory.FreeGroup.R... |
3,989 | lean_file_chunk | 24a32f507cb648f7600908c09154f65f76b93f66f187f4bbad04841b1aacde28 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Christian Krause. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Krause
-/
module
public import Mathlib.GroupTheory.FreeGroup.Reduce
public import Mathlib.GroupTheory.GroupAction.Defs
/-!
For any `w : α × Bool`, `FreeGroup.startsWith w... |
1,734 | lean_file_chunk | 1134bc803f30a6169c03460db4591d8462e5b2378873ec6913f21836c00d6ee9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Algebra.FreeAbelianGroup.Finsupp
public import Mathlib.GroupTheory.FreeGroup.IsFreeGroup
public import Mathlib.LinearAlgebra.Dimension.S... |
13,419 | lean_file_chunk | 26f9113e3d4c22eb861e60725c37ba000d572b029b7d6de06f9055742a4ac7c2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
module
public import Mathlib.CategoryTheory.Action
public import Mathlib.Combinatorics.Quiver.Arborescence
public import Mathlib.Combinatorics.Quiver.ConnectedComponent
publ... |
14,440 | lean_file_chunk | b82a2c09c079231194656d7b15cd068defd1a450662835e45dabbd43623d4f84 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
module
public import Mathlib.Data.Finset.Dedup
public import Mathlib.Data.Fintype.Defs
public import Mathlib.Data.List.Sublists
public import Mathlib.GroupTheory.FreeGroup.Bas... |
2,107 | lean_file_chunk | 633c9f0c0da077e4f41cded9a24e547d99430dd70993dec9eed30e456f25530e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Algebra.Group.Subgroup.Ker
/-!
# Saturated subgroups
## Tags
subgroup, subgroups
-/
@[expose] public section
namespace Submonoid
... |
4,430 | lean_file_chunk | c8d228b08c561971fb80de0d84daa4d18d6e1d9282016ae41f879694705fb88f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
module
public import Mathlib.Algebra.Group.Subgroup.Basic
public import Mathlib.GroupTheory.Submonoid.Center
/-!
# Centers of subgroups
-/
@[expose] public section
ass... |
2,798 | lean_file_chunk | 89200d4d0bb59bdbcf61444da68e6e17adb67ca05291b1f57bd7754fe0bc003f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
module
public import Mathlib.Order.Atoms
public import Mathlib.Algebra.Group.Subgroup.Basic
/-!
# Simple groups
This file defines `IsSimpleGroup G`, a class indica... |
7,694 | lean_file_chunk | c73d641db1388b9e1bece3d4bd0fe74acbfe64f67354c058efeb666af8710f26 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
module
public import Mathlib.Algebra.Group.Action.End
public import Mathlib.Algebra.Group.Commutator
public import Mathlib.GroupTheory.Subgroup.Center
public import Mathli... |
2,137 | lean_file_chunk | 6c9133725f1862c62908845894aa8e1ab36252bae8981318544b5007da0a88a3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Jireh Loreaux
-/
module
public import Mathlib.Algebra.Group.Center
public import Mathlib.Algebra.Group.Subsemigroup.Defs
/-!
# Centers of semigroups, as subsemigroups.
## ... |
3,484 | lean_file_chunk | 7ff2982ea6db67b49f2e9a1814e05faf650e5e833dc76a3135e8b6198870d389 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Jireh Loreaux
-/
module
public import Mathlib.Algebra.Group.Center
public import Mathlib.Algebra.Group.Subsemigroup.Basic
public import Mathlib.GroupTheory.Subsemigr... |
23,969 | lean_file_chunk | 627df3dad649ef45ef14283f17df352a21bb9ab3f63edda55fc9936383f6a4dc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Yaël Dillies
-/
module
public import Mathlib.Data.List.Iterate
public import Mathlib.Data.Set.Pairwise.List
public import Mathlib.GroupTheory.Perm.Cycle.Basic
public impor... |
13,839 | lean_file_chunk | 2a4c2450bf1a6845d6372ca25b1bea06368a9e11df4163cf4b7c6d76c7e0854e | lean_source_file | pkg_mathlib_source_file_chunks | lemma cycleOf_ne_one_iff_mem_cycleFactorsFinset {g : Equiv.Perm α} {x : α} :
g.cycleOf x ≠ 1 ↔ g.cycleOf x ∈ g.cycleFactorsFinset := by
rw [cycleOf_mem_cycleFactorsFinset_iff, mem_support, ne_eq, cycleOf_eq_one_iff]
theorem mem_cycleFactorsFinset_support_le {p f : Perm α} (h : p ∈ cycleFactorsFinset f) :
p.s... |
23,933 | lean_file_chunk | 8b5dd2d9eb72dac88202f5dce010c71603c6906ca16ea48ed0dcbef994d3d413 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
module
public import Mathlib.Algebra.GCDMonoid.Multiset
public import Mathlib.Algebra.GCDMonoid.Nat
public import Mathlib.Algebra.Group.TypeTags.Finite
public impo... |
9,510 | lean_file_chunk | 8c94f5cfcb6baf40fefe7ee4ebbd0e335e1e79f597262fe5b8c975af81614fa7 | lean_source_file | pkg_mathlib_source_file_chunks | theorem _root_.exists_prime_addOrderOf_dvd_card {G : Type*} [AddGroup G] [Fintype G] (p : ℕ)
[Fact p.Prime] (hdvd : p ∣ Fintype.card G) : ∃ x : G, addOrderOf x = p :=
@exists_prime_orderOf_dvd_card (Multiplicative G) _ _ _ _ (by convert hdvd)
attribute [to_additive existing] exists_prime_orderOf_dvd_card
-- TOD... |
23,972 | lean_file_chunk | c3eb21f5c49325df938b2a5e83be75e14c6ace6694792a553891d39f60915f5c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Yaël Dillies
-/
module
public import Mathlib.Algebra.Module.BigOperators
public import Mathlib.GroupTheory.Perm.Basic
public import Mathlib.GroupTheory.Perm.Finite
public ... |
18,754 | lean_file_chunk | 6efeb67c002e3e89974da431ca13e28085e94e2c6d778334f02e8ad773e4b38f | lean_source_file | pkg_mathlib_source_file_chunks | cases nonempty_fintype β
have : n.Coprime (orderOf f) := by
refine Nat.Coprime.symm ?_
rw [Nat.Prime.coprime_iff_not_dvd hf']
exact Nat.not_dvd_of_pos_of_lt hn hn'
exact (pow_iff hf).mpr this
end IsCycle
open Equiv
theorem _root_.Int.addLeft_one_isCycle : (Equiv.addLeft 1 : Perm ℤ).IsCycle ... |
20,403 | lean_file_chunk | 80a1491d1f379e6e6059bd4cebbfa049119183387ccc6d33f46535c1ee9fed01 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Data.List.Cycle
public import Mathlib.GroupTheory.Perm.Cycle.Type
public import Mathlib.GroupTheory.Perm.List
/-!
# Properties of cy... |
4,127 | lean_file_chunk | a1e50438a2ef3aad9a2f47129891ccd46045b6d2658d6fd5de6062c6850174a1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.GroupTheory.Perm.Cycle.Concrete
/-! # Possible cycle types of permutations
* For `m : Multiset ℕ`, `Equiv.Perm.exists_wi... |
10,071 | lean_file_chunk | c8e967036179631b2f8a6580d96d75a1f6f7e2702bb3fae416298ab7116959a0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.GroupTheory.GroupAction.Basic
public import Mathlib.GroupTheory.GroupAction.Embedding
public import Mathlib.GroupTheory.Gr... |
11,958 | lean_file_chunk | e5a9af8ce211bdc8696246e7af5b64c1e70fc3b93fc28e3e6f26cc9193571fcf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.Data.Set.PowersetCard
public import Mathlib.GroupTheory.SpecificGroups.Alternating.MaximalSubgroups
/-! # Combinations
... |
3,227 | lean_file_chunk | f830e5b352ebef68e72903bfb122565d1d9a2f18b3adfae6988e477b7440d8df | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.GroupTheory.GroupAction.SubMulAction
public import Mathlib.Algebra.Group.Pointwise.Set.Basic
/-!
# Pointwise monoid structures on SubMulActio... |
1,691 | lean_file_chunk | 233147ff5768c9027a478faaa69d4f756b95b0c5dedae5be47551276b2081271 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Dexin Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dexin Zhang
-/
module
public import Mathlib.Data.Set.Finite.Basic
public import Mathlib.Data.Set.Lattice
public import Mathlib.GroupTheory.GroupAction.SubMulAction
/-!
# Closure and fin... |
21,118 | lean_file_chunk | e5ba42be549a7e3ad08a238b73f0114fc855fd30ec03b1a49d9dd2184a61e041 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.Algebra.Group.Pointwise.Set.Card
public import Mathlib.GroupTheory.GroupAction.FixingSubgroup
public import Mathlib.GroupT... |
2,747 | lean_file_chunk | d724a9037086bec7646c52263838e63712cbc6b983e2994153ddd2581dbfa4e0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.GroupTheory.GroupAction.DomAct.Basic
public import Mathlib.GroupTheory.GroupAction.Hom
/-!
# Action of `Mᵈᵐᵃ` on `α →[N] β` and `A →+[... |
10,525 | lean_file_chunk | f9484c5fd7d345c207d1593205d57dc31d63ab4cc5e2e821273c85629dc4764b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Algebra.Group.Action.Basic
public import Mathlib.Algebra.Group.Opposite
public import Mathlib.Algebra.Group.Pi.Lemmas
public import Ma... |
17,573 | lean_file_chunk | 42e6fc6af89ada55598b96741b355cd9d111bfa88edead929d5f1987282d797c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
module
public import Mathlib.Data.ZMod.QuotientGroup
/-!
# Cyclic groups
`IsCyclic` is a predicate on a group stating that the group is cyclic.
For the concrete cy... |
12,656 | lean_file_chunk | e31d58f5982737fbedf2b1b815c854f87d66ee215e34f61ea9d3511f8300e95d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.GroupTheory.GroupAction.SubMulAction
public import Mathlib.GroupTheory.Perm.MaximalSubgroups
public import Mathlib.GroupTh... |
9,982 | lean_file_chunk | e69ce1b351e8c94b9c63cd5054f21385b142da62289b7267fe5b8674140cd9be | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.GroupTheory.SpecificGroups.Alternating.Centralizer
public import Mathlib.GroupTheory.SpecificGroups.KleinFour
public impor... |
12,702 | lean_file_chunk | a4ac282611bb1af66cee50eb3ce899e1c2b6acfc8ca5b233c8fe6710922acdc6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.GroupTheory.Perm.Centralizer
public import Mathlib.GroupTheory.SpecificGroups.Alternating
/-! # Centralizer of an element... |
7,334 | lean_file_chunk | 71eb78046e68088085de3bab4e847f07c8d20f2bfd5343497f72d94ab4e51a12 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.MorphismProperty.Limits
/-!
# Attaching cells
Given a family of morphisms `g a : A a ⟶ B a` and a morphism `f : X₁ ⟶ X₂`,
we intr... |
4,047 | lean_file_chunk | 37620106759d266bc704bd5e75148fa79600edac6222ade60be419860c723d14 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.RelativeCellComplex.AttachCells
public import Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition
/-!
# Relative cel... |
5,615 | lean_file_chunk | c7f0527213142e35504c358026cd9efdc6d5b34c39e881fb961ba10680ffdf73 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.DoldKan.FunctorN
/-!
# Comparison with the normalized Moore complex functor
In this file, we show that when the category `A` ... |
5,181 | lean_file_chunk | a3e57af162fc75d5fbddbc298fcb2ad7d29f163167dfc78d91f0abc2934f27cb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.DoldKan.PInfty
/-!
# Decomposition of the Q endomorphisms
In this file, we obtain a lemma `decomposition_Q` which expresses
e... |
13,770 | lean_file_chunk | 78747676ea5573912370a46c4b74965176d688aed4612093ac0d78b3e7a1befd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.SimplicialObject.Split
public import Mathlib.AlgebraicTopology.DoldKan.PInfty
/-!
# Construction of the inverse functor of the... |
3,651 | lean_file_chunk | df9874d8f513d148209f69724cc3afefbdfa2ac1f0d68758f87c88e0560927ff | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.DoldKan.Normalized
/-!
# The normalized Moore complex and the alternating face map complex are homotopy equivalent
In this fi... |
10,906 | lean_file_chunk | 9730f38ea8718343aec7f78c30a46ce42536e884012f9877ffe2e2b572ecff2f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.SimplicialObject.Split
public import Mathlib.AlgebraicTopology.DoldKan.Degeneracies
public import Mathlib.AlgebraicTopology.Dold... |
5,068 | lean_file_chunk | d3fc576584a820087f740ac76714794de5245fbd5524540966a1b08ce588f741 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.DoldKan.FunctorN
public import Mathlib.AlgebraicTopology.DoldKan.Decomposition
public import Mathlib.CategoryTheory.Idempotents.... |
7,278 | lean_file_chunk | 53be7173bc7aabc70a92b6b3b801f4a3e71003269121c801ebac5a90f6101a08 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.DoldKan.Faces
public import Mathlib.CategoryTheory.Idempotents.Basic
/-!
# Construction of projections for the Dold-Kan corres... |
8,205 | lean_file_chunk | cb917ab41639ef1858c07855e8fb3bae2a3726db713f710c1182c6def2ee5eda | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.DoldKan.Homotopies
public import Mathlib.Tactic.Ring
/-!
# Study of face maps for the Dold-Kan correspondence
In this file, w... |
7,420 | lean_file_chunk | 42dfb10180b30f82c3c2d52f1999c62dec83e3a2b94d619fa6c34ffa2498d652 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.DoldKan.FunctorGamma
public import Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject
public import Mathlib.CategoryTheory.... |
5,767 | lean_file_chunk | 0a1c6602d279e6d0c5b4993f5c123e3c1f2e7cbc7228009ffe846f28daa947d7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.DoldKan.Decomposition
public import Mathlib.Tactic.FinCases
public import Mathlib.Tactic.Linarith
/-!
# Behaviour of `P_infty`... |
8,306 | lean_file_chunk | 7f339fcf90ff58fe7d774bd3cd80af9cdb23ca8dba0cbcab14952f1337acb81c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.Algebra.Homology.Homotopy
public import Mathlib.AlgebraicTopology.DoldKan.Notations
/-!
# Construction of homotopies for the Dold-Kan correspond... |
9,983 | lean_file_chunk | 99a6a74b4ccc8c97c8985b8744506ed10252030f3380d538ebbfc7fc31a1347f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.DoldKan.GammaCompN
public import Mathlib.AlgebraicTopology.DoldKan.NReflectsIso
/-! The unit isomorphism of the Dold-Kan equiva... |
7,529 | lean_file_chunk | 3bfa47898f8cdfedf542067903146fb269d4c59e704df914805edbd7200ee06b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.DoldKan.Projections
public import Mathlib.CategoryTheory.Idempotents.FunctorCategories
public import Mathlib.CategoryTheory.Idem... |
5,771 | lean_file_chunk | a782b32c07d405944ce1981855cc458119d26f588d6ef69a3949a249f4551272 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.DoldKan.EquivalenceAdditive
public import Mathlib.AlgebraicTopology.DoldKan.Compatibility
public import Mathlib.CategoryTheory.I... |
8,467 | lean_file_chunk | f659ec2eabb2fd3086fd73d85e95a4842fa5173c2064b267de7622f6942d3a68 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.DoldKan.EquivalencePseudoabelian
public import Mathlib.AlgebraicTopology.DoldKan.Normalized
/-!
# The Dold-Kan correspondence
... |
1,930 | lean_file_chunk | 0cf69464743754ac4a65c53b8c3e6fa02039271abae76123c0bff24771dd47bc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.DoldKan.NCompGamma
/-! The Dold-Kan equivalence for additive categories.
This file defines `Preadditive.DoldKan.equivalence` w... |
831 | lean_file_chunk | 12009aeca7e0fba025a71c857561d5ee02251787642a9749c8a1312742678934 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.AlternatingFaceMapComplex
/-!
# Notations for the Dold-Kan equivalence
This file defines the notation `K[X] : ChainComplex C ... |
2,713 | lean_file_chunk | 8c8238eaf51181f21984b9369b3225f730e1b47799beacbc2baaafc1ebcdadde | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.DoldKan.PInfty
/-!
# Construction of functors N for the Dold-Kan correspondence
In this file, we construct functors `N₁ : Sim... |
11,764 | lean_file_chunk | 9eaa235e580d46fd38f5037387c18acd0a3fd86a4e25b57878d1e3aaa71db52f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Equivalence
/-! Tools for compatibilities between Dold-Kan equivalences
The purpose of this file is to introduce tools which will... |
8,048 | lean_file_chunk | 04a26a93df9cd538e5e590032a77b09f7e2e004593ca82dc48fe3bb1a0298411 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Praneeth Kolichala. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Praneeth Kolichala
-/
module
public import Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps
public import Mathlib.Topology.Homotopy.Contractible
public import Mathlib.Cat... |
1,204 | lean_file_chunk | 833dbed9c805693ebb1ffa6c2b1eb7690ec417f560db2e1f32a37eb3a863ffdd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Praneeth Kolichala. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Praneeth Kolichala
-/
module
public import Mathlib.CategoryTheory.PUnit
public import Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic
/-!
# Fundamental groupoid of punit
The... |
7,161 | lean_file_chunk | ce08b7b1b2816f13944b42e2b76939588bcd5203e349ebef2c60f8713a4d124b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Praneeth Kolichala. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Praneeth Kolichala
-/
module
public import Mathlib.CategoryTheory.Groupoid
public import Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic
public import Mathlib.Topology.Categor... |
13,620 | lean_file_chunk | 338f8303784649057926575fa8ace4be94c6e50720e90c12e76054080cd5e133 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Shing Tak Lam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shing Tak Lam
-/
module
public import Mathlib.CategoryTheory.Groupoid.Grpd.Basic
public import Mathlib.Topology.Category.TopCat.Basic
public import Mathlib.Topology.Homotopy.Path
publi... |
11,112 | lean_file_chunk | f66428c37a1c145fc309233ed02b4a4aba0a59e8a072adccef179bc9a56b4e51 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Praneeth Kolichala. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Praneeth Kolichala, Yury Kudryashov
-/
module
public import Mathlib.Topology.Homotopy.Equiv
public import Mathlib.CategoryTheory.Equivalence
public import Mathlib.AlgebraicTopolog... |
3,319 | lean_file_chunk | 807a6687c40eaa3a096254598323a71a6bb235acf73c9cda42b6fc757fc24a83 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Mark Lavrentyev. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mark Lavrentyev
-/
module
public import Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic
public import Mathlib.CategoryTheory.Conj
public import Mathlib.CategoryTheory.Groupoid
pu... |
1,261 | lean_file_chunk | 013598f249a4f3f9e40a5701b929a8a9a607c1c02b862625faff96d3fbdbc0bd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.SimplicialCategory.Basic
public import Mathlib.CategoryTheory.Functor.FunctorHom
/-!
# The category of simplicial objects is si... |
2,392 | lean_file_chunk | a4935a1543745f8954b7b51dcda53a087802340c89f7bbe0415f3747222156fa | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.SimplicialSet.Monoidal
public import Mathlib.CategoryTheory.Enriched.Ordinary.Basic
/-!
# Simplicial categories
A simplicial c... |
7,976 | lean_file_chunk | 5f695c3fec0a66837dc88f099d56747ce2e30dfd7a5f7248b4f2a755564f790f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Fabian Odermatt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabian Odermatt
-/
module
public import Mathlib.AlgebraicTopology.SimplicialObject.Homotopy
public import Mathlib.AlgebraicTopology.AlternatingFaceMapComplex
public import Mathlib.Al... |
12,910 | lean_file_chunk | 62d25f0bfdabd141247cc58954766fca1a0eb1e5d6dd9979fbaabbd3e3bd4f03 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.SimplicialObject.Basic
public import Mathlib.CategoryTheory.Limits.Shapes.Products
public import Mathlib.Data.Fintype.Sigma
/-!... |
3,198 | lean_file_chunk | 3a0d691025a59870a4a7a9361b80416121ace8d1afd9fbae5eba1b520641faf5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.SimplexCategory.Rev
public import Mathlib.AlgebraicTopology.SimplicialObject.Basic
/-!
# The covariant involution of the catego... |
23,995 | lean_file_chunk | 68e6882e4239d5735210f4b76228b27413de61acaea2043abd76da8639a160e5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kim Morrison, Adam Topaz
-/
module
public import Mathlib.AlgebraicTopology.SimplexCategory.Basic
public import Mathlib.CategoryTheory.Adjunction.Reflective
public import... |
8,898 | lean_file_chunk | c460f3a0e142f6d0912b34290c8599f8c1ea8ed9a222ac56dea10c74b92c31d1 | lean_source_file | pkg_mathlib_source_file_chunks | set_option backward.isDefEq.respectTransparency false in
instance {n} {J : Type v} [SmallCategory J] [HasColimitsOfShape J C] :
HasColimitsOfShape J (CosimplicialObject.Truncated C n) := by
dsimp [Truncated]
infer_instance
instance {n} [HasColimits C] : HasColimits (CosimplicialObject.Truncated C n) :=
⟨infe... |
9,569 | lean_file_chunk | 8be7b571cf85181d483af8ed12fb98a2bca3a9f60f7fe79eb048d67081b57f2e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.SimplicialObject.Basic
/-!
# A construction by Gabriel and Zisman
In this file, we construct a cosimplicial object `SimplexCat... |
3,258 | lean_file_chunk | 6c6dcdf864221416831aeb3c545e83647082f79abc6c953d88f7909c3c4852b4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Emily Riehl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Emily Riehl, Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.SimplicialObject.Basic
public import Mathlib.CategoryTheory.Functor.KanExtension.Adjunction
publi... |
6,994 | lean_file_chunk | ffdc47a74032c05bae24ff033e2a2b9a3e58c7c1d69f1ff0fd66f3a72eddff4b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Fabian Odermatt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabian Odermatt
-/
module
public import Mathlib.AlgebraicTopology.SimplicialObject.Basic
public import Mathlib.AlgebraicTopology.SimplexCategory.Basic
/-!
# Simplicial homotopies of... |
8,351 | lean_file_chunk | 33a86288e3e12ae40464dc16e2e614f0914399e03b8b69232748a86d1eb384d1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.MorphismProperty.Composition
/-!
# Categories with classes of fibrations, cofibrations, weak equivalences
We introduce typeclasse... |
12,293 | lean_file_chunk | 1d7538ba3e6c7778ffe816e4cf79345f8ffbd42b6420b5f4c73600c82e4c7ff5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.MorphismProperty.WeakFactorizationSystem
public import Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations
/-!
# Cons... |
1,620 | lean_file_chunk | b53506b6ea0788a96d583a458a5a2ad040cb2bb2321239b975044f2ab92215c2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.ModelCategory.Basic
/-!
# The opposite of a model category structure
-/
@[expose] public section
universe v u
open Category... |
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