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 |
|---|---|---|---|---|---|
3,749 | lean_file_chunk | 1ecb87c93245a02c6dfc1fea991a4159b4f91101d9640b5d25b8d1c326b68cef | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Gaëtan Serré. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gaëtan Serré
-/
module
public import Mathlib.CategoryTheory.CopyDiscardCategory.Basic
public import Mathlib.CategoryTheory.Localization.Monoidal.Basic
public import Mathlib.CategoryThe... |
17,492 | lean_file_chunk | bd72d43b1ec9ea37d2758f74e58715fb2b305674686098fb91cdfdbdd7cbf171 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Monoidal.Functor
/-!
# Constructing monoidal functors from natural transformations between multifunctors
This file ... |
15,017 | lean_file_chunk | 226b4b0a22c505515f3537ab1aca6f91073e238ed0da3330b107011aba411878 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Lean FRO LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Monoidal.Mon_
public import Mathlib.CategoryTheory.Monoidal.Braided.Opposite
public import Mathlib.CategoryTheory.Monoidal.Tr... |
2,234 | lean_file_chunk | deaa87e4fa2645c5ac4e755be9920d7a37ad392af44171a8ed8969634e2c6eaa | 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: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Abelian.LeftDerived
public import Mathlib.CategoryTheory.Monoidal.Preadditive
/-!
# Tor, the left-derived functor of tensor ... |
7,196 | lean_file_chunk | e615b863691157fbc4984baed8f5f470e201c3ce27b120bd615ee372ce7116a0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Jack McKoen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jack McKoen
-/
module
public import Mathlib.CategoryTheory.Monoidal.Closed.Braided
public import Mathlib.CategoryTheory.Monoidal.Limits.HasLimits
public import Mathlib.CategoryTheory.Mon... |
23,965 | lean_file_chunk | 412e9d7d04a0aa751cf977620b085a319a4918162d54893514c65425696d904f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Algebra.Group.PUnit
public import Mathlib.CategoryTheory.Monoidal.Braided.Basic
public import Mathlib.CategoryTheory.Monoidal.CoherenceLemma... |
22,170 | lean_file_chunk | 572abdbc06d3071c914e326deabaaedf41dcb17fcd19d5e8026380731cc995b7 | lean_source_file | pkg_mathlib_source_file_chunks | set_option backward.isDefEq.respectTransparency false in
@[to_additive (attr := simps)]
instance uniqueHomFromTrivial (A : Mon C) : Unique (trivial C ⟶ A) where
default.hom := η[A.X]
default.isMonHom_hom.mul_hom := by simp [unitors_equal]
uniq f := by
ext
rw [← Category.id_comp f.hom]
dsimp only [triv... |
8,291 | lean_file_chunk | 71b3676866a33470698f846b4bf6fe92dccc5f4e4ddfd32485fd54e0ea77b5ab | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Monoidal.Braided.Basic
public import Mathlib.CategoryTheory.Functor.Category
public import Mathlib.CategoryTheory.Functor.Con... |
9,800 | lean_file_chunk | 3438462727942ab2d1a298931f46c617397bff13badae74c206c58db74ac0d9b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Lean FRO LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Monoidal.Comon_
/-!
# The category of bimonoids in a braided monoidal category.
We define bimonoids in a braided monoidal c... |
8,525 | lean_file_chunk | efb403ab7d6780010608ebe338c5a570d43cc34d779ef121911cc27a1136042c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour
-/
module
public import Mathlib.CategoryTheory.Pi.Basic
public import Mathlib.CategoryTheory.Monoidal.Category
public import Mathlib.CategoryTheory.Monoidal.Braided.B... |
10,848 | lean_file_chunk | 2eaccd0b86e21b730c959196e3f4a2b33aae5027bee84d65b84651e00cfd01e2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Kim Morrison
-/
module
public import Mathlib.CategoryTheory.EqToHom
public import Mathlib.CategoryTheory.NatIso
public import Mathlib.CategoryTheory.Products.Basic
/-!
# C... |
11,982 | lean_file_chunk | 2917de7a9776d2b5ab4617c56f9fe81e11fd4aabb0ba4061dd667e5d6360c6d1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Algebra.BigOperators.Fin
public import Mathlib.CategoryTheory.Monoidal.Linear
public import Mathlib.CategoryTheory.Monoidal.Rigid.FunctorCat... |
15,845 | lean_file_chunk | e3d540cf1d9e6c2a8f55dd8b3304aa3407640b2105c1878e77285da28125d2a3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Algebra.Category.Grp.Basic
public import Mathlib.Algebra.Ring.PUnit
public import Mathlib.CategoryTheory.Adjunction.Limits
public import Mat... |
8,194 | lean_file_chunk | cdf216b429b17a3f68e15a5bc52c0b67f88fa2949703b4a3823fd250debe20d6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.CategoryTheory.Action.Basic
public import Mathlib.Topology.Algebra.MulAction
public import Mathlib.Topology.Category.TopCat.Basic
pu... |
16,830 | lean_file_chunk | 60d0eec09c5fdd6109f0b22ac57cc0936c7939d99aab8e67f7b6e309fd24fd1f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Abelian.FunctorCategory
public import Mathlib.CategoryTheory.Abelian.Transfer
public import Mathlib.CategoryTheory.Linear.Lin... |
8,045 | lean_file_chunk | 1cece4d592c26eaa558dac97a7366c45c43b054e8f1e4a6e638d96a71215cbb0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Algebra.Group.Action.End
public import Mathlib.Algebra.Group.Action.Pi
public import Mathlib.CategoryTheory.Action.Basic
public import Mathl... |
3,984 | lean_file_chunk | 415755f16c4a7b7694da7078fce71356d9aeb694f5cd58c2d2abdd428d2f3045 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Equivalence
public import Mathlib.CategoryTheory.Adjunction.Mates
/-!
# Functoriality of the symmetry of equivalences
Usi... |
5,629 | lean_file_chunk | 5f090dbce5dd709f090f9f2ec751af2e58d9cc6fb987698a82e6ec32de5a6a3d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Daniel Carranza. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Carranza
-/
module
public import Mathlib.CategoryTheory.Enriched.Ordinary.Basic
public import Mathlib.CategoryTheory.Monoidal.Braided.Basic
/-!
# The opposite category of an... |
4,082 | lean_file_chunk | 0d729bfeafd667997ee008f5fbe197ca62dee8309a8aa8287d537c37b98117c9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Nick Ward. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nick Ward
-/
module
public import Mathlib.CategoryTheory.Enriched.Ordinary.Basic
/-!
# Congruence of enriched homs
Recall that when `C` is both a category and a `V`-enriched category, we... |
19,582 | lean_file_chunk | adf9ea008d5f4705ee706f4974aa7bdb8e9135301c8cd7654723997e663b3e55 | 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: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Monoidal.Types.Coyoneda
public import Mathlib.CategoryTheory.Monoidal.Center
public import Mathlib.Tactic.ApplyFun
/-!
# Enr... |
4,623 | lean_file_chunk | 65c7a83e0ec51438682234ac7d01c554300f322d14f3a0a41e674a04ab9f8d65 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
module
public import Mathlib.CategoryTheory.Enriched.Basic
public import Mathlib.CategoryTheory.Bicategory.Basic
/-!
# The bicategory of `V`-enriched categories... |
20,307 | lean_file_chunk | 8a849ff5835e7dfe17c5b77592eb9d08bd06156a02ce4eb70e8b881e6a064e2b | 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.Monoidal.FunctorCategory
public import Mathlib.CategoryTheory.Enriched.Ordinary.Basic
public import Mathlib.CategoryTheory.Functor.... |
10,185 | lean_file_chunk | fd6c696bb658373a8a57df7be8bcb139b50841b8746d862cfce6d2da4120ae7c | 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: Kim Morrison, Robin Carlier
-/
module
public import Mathlib.CategoryTheory.EqToHom
public import Mathlib.CategoryTheory.Quotient
public import Mathlib.Combinatorics.Quiver.Path
/-!
# T... |
2,889 | lean_file_chunk | d25a0f77c4eba356457a47a0fcfcdf1fd809a10e887b75389a798d418ae3f856 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
module
public import Mathlib.CategoryTheory.PathCategory.Basic
public import Mathlib.CategoryTheory.MorphismProperty.Composition
/-!
# Properties of morphisms in a pa... |
846 | lean_file_chunk | 94c140fcf854e7966e490978017d34fdbf6a00226e5804eee212aeb0007bb2ab | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Dénes Pápai. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dénes Pápai
-/
module
public import Mathlib.CategoryTheory.Adhesive.Basic
public import Mathlib.CategoryTheory.Limits.Constructions.Over.Connected
/-! # Adhesive structure on slice cate... |
23,910 | lean_file_chunk | 977e6f7a70d297d757c004a61249c70a8480b41ecdd194f7bcaaa81e00f59091 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Jack McKoen
-/
module
public import Mathlib.CategoryTheory.Extensive
public import Mathlib.CategoryTheory.Limits.Shapes.KernelPair
public import Mathlib.CategoryTheory.Limit... |
192 | lean_file_chunk | eafec0bae27e8f225c73318e32af9fcf99c9f9d2ac2eabc509ce4f5825c33d8a | lean_source_file | pkg_mathlib_source_file_chunks | · exact isColimitOfPreserves Gl ((IsColimit.precomposeHomEquiv _ _).symm <| pushoutIsPushout _ _)
· exact (IsColimit.precomposeHomEquiv _ _).symm H.isColimit
end functor
end CategoryTheory |
1,736 | lean_file_chunk | 2ede4ed670a1c730f45aa404eb60ada013be5257961320a0d224905382892594 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Jack McKoen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jack McKoen
-/
module
public import Mathlib.CategoryTheory.Adhesive.Basic
public import Mathlib.CategoryTheory.Subobject.Basic
public import Mathlib.CategoryTheory.Subobject.Lattice
/-!... |
590 | lean_file_chunk | 82e6c2faceb66173f221190758a85c5536c01f9bea95d0d624de340238312357 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 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.EssentiallySmall
public import Mathlib.CategoryTheory.Quotient
/-!
# Quotient categories are locally small
-/
@[expose] public s... |
4,665 | lean_file_chunk | b7dfe33c7bfbd51212559c29987dfef9eaa2ef1d7bc4c5ef87da713471477083 | 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.Quotient
public import Mathlib.CategoryTheory.Linear.LinearFunctor
/-!
# The quotient category is linear
If `r : HomRel C` is a c... |
3,356 | lean_file_chunk | 328fdda3066a11cfa9ef7d79360fc6874de7f03927488e3dbcd69aee9a0c5175 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 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.Quotient
public import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
/-!
# The quotient category is preadditive
If an equiva... |
7,406 | lean_file_chunk | 92f0e4ae9394bc34944e5cb32ca32f1ee56819290a4f04961f6ba4c46872e379 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Sums.Associator
public import Mathlib.CategoryTheory.Products.Associator
/-!
# Functors out of sums of categories.
This f... |
11,939 | lean_file_chunk | 6a2ef54648793ee49be7fb552f314552c469b0afac8d23faa5c93fbc73e3ba7f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Equivalence
/-!
# Binary disjoint unions of categories
We define the category instance on `C ⊕ D` when `C` a... |
7,889 | lean_file_chunk | bf63a202d805c83e9ed591e88da4da620b623ca6979cec7f700f24a00dcedd32 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Sums.Basic
/-!
# Associator for binary disjoint union of categories.
The associator functor `((C ⊕ D) ⊕ E) ⥤... |
7,751 | lean_file_chunk | 6c02a19cce462cc66f15b8f0ce8267ea5e5703101ec357002fd1fc485f4fe14a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.CategoryTheory.Subobject.Lattice
public import Mathlib.CategoryTheory.Monoidal.Braided.Basic
public import Mathlib.CategoryTheory.Dialec... |
4,923 | lean_file_chunk | 270039395bc6986a08e199e584a36348fb2f77ead44d3c3e419ee1dfb802cf4f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.CategoryTheory.Subobject.Basic
public import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts
/-!
# Dialectica category
We define t... |
5,608 | lean_file_chunk | a14bf3515cd2a7242f19914051b607e7b9b5a34c9fef9f54b34c4dc0e849dafc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.CategoryTheory.Galois.Action
/-!
# Fiber functors are (faithfully) full
Any (fiber) functor `F : C ⥤ FintypeCat` factors via the ... |
13,922 | lean_file_chunk | 0c241b5a6903c304e47ea9f410e09d409d9cb48d0889144ae66574a5f75c7471 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.CategoryTheory.Galois.GaloisObjects
public import Mathlib.CategoryTheory.Limits.Shapes.CombinedProducts
public import Mathlib.Data.F... |
8,806 | lean_file_chunk | 779ad05cdacd960b9730d0b58cdc4cba19940966dea792925018864420a309f6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.CategoryTheory.Galois.Prorepresentability
public import Mathlib.Topology.Algebra.ContinuousMonoidHom
public import Mathlib.Topology.... |
20,803 | lean_file_chunk | 53d1a36fe64a8fe7875394f4d1c8b11e0e80e86e228e0a5f44dd6c392b0c1945 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.Algebra.Group.TransferInstance
public import Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers
public import... |
18,978 | lean_file_chunk | 943d0ed88767316996c56d0d4ff3135860cc56b3516b6794ebfaec27eb1712f5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.Algebra.Category.Grp.Limits
public import Mathlib.CategoryTheory.CofilteredSystem
public import Mathlib.CategoryTheory.Galois.Decomp... |
12,645 | lean_file_chunk | c489124808e7036fca387abb0647c41bcd2702d211bd9ffeb182ecfd476e312a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.CategoryTheory.Galois.Full
public import Mathlib.CategoryTheory.Galois.Topology
public import Mathlib.Topology.Algebra.OpenSubgroup
... |
3,326 | lean_file_chunk | bccef9923909aa614dddead4bed59c8355d2f299de277996b05d66031a94def4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.CategoryTheory.Galois.Examples
public import Mathlib.CategoryTheory.Galois.Prorepresentability
/-!
# Induced functor to finite `Au... |
11,528 | lean_file_chunk | 70ae06ee9fdfe42ce7ff7a973ac0e83b2dd9f73080f5fb9c959dcc8677bc7b13 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.CategoryTheory.Galois.Basic
public import Mathlib.CategoryTheory.Galois.Topology
public import Mathlib.CategoryTheory.Galois.Prorepr... |
7,843 | lean_file_chunk | 09bc6240b1744d212c9ebf189c74344e05267204ff3056199d73834f17e9eca2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.CategoryTheory.Galois.Basic
public import Mathlib.CategoryTheory.Action.Concrete
public import Mathlib.CategoryTheory.Action.Limits
... |
3,524 | lean_file_chunk | 0896f26b8f3c3d3133c2efccdaae15a7a1303fed00c5a30a6072155cf648de69 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.CategoryTheory.Galois.EssSurj
public import Mathlib.CategoryTheory.Action.Continuous
public import Mathlib.Topology.Category.FinTopC... |
8,993 | lean_file_chunk | 1811331bd034a19bf2a8f8d150acf85279dd294b609a1b0e77fc848df318cb9e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.CategoryTheory.Galois.Basic
public import Mathlib.CategoryTheory.Limits.FintypeCat
public import Mathlib.CategoryTheory.Limits.Prese... |
4,707 | lean_file_chunk | a01f370061523874d07e98ea437795954d78b1c2e2c8cb6c252a50c8f49b6090 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne
-/
module
public import Mathlib.CategoryTheory.Bicategory.FunctorBicategory.Pseudo
public import Mathlib.CategoryTheory.Bicategory.Opposites
/-!
# 2-Yoneda embedding
In thi... |
9,345 | lean_file_chunk | f43fa45b4b25578f07993d36c1ace66150815e0ef6a52f70ca6734c7b77ea766 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno, Junyan Xu
-/
module
public import Mathlib.CategoryTheory.PathCategory.Basic
public import Mathlib.CategoryTheory.Functor.FullyFaithful
public import Mathlib.CategoryTheory.B... |
3,353 | lean_file_chunk | dceae9533dcfceeb4c8ce46084823daddae5db8cb15e17f2d11893a4f87b81cd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne
-/
module
public import Mathlib.CategoryTheory.Bicategory.Functor.StrictPseudofunctor
/-!
# Cartesian products of bicategories
We define the bicategory instance on `B × C` ... |
11,708 | lean_file_chunk | 7863e5967aebc5d1f594fc4342a57d65bdeabbda56112fcc8f35ec637086ddd1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
module
public import Mathlib.CategoryTheory.Bicategory.Basic
public import Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
public import Mathlib.Tactic.CategoryTheory.C... |
21,605 | lean_file_chunk | e0f71d279922d41f2c399261885e5f175907d5b92887efc6f156a420c0e9a8af | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
module
public import Mathlib.CategoryTheory.NatIso
/-!
# Bicategories
In this file we define typeclass for bicategories.
A bicategory `B` consists of
* objects `a : B`,... |
1,384 | lean_file_chunk | 013c64105485a743e25da17363413054ee7a5d8fbff0e61e6a1e1592b1d04406 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Bicategory.Basic
public import Mathlib.CategoryTheory.Monoidal.Category
/-!
# Endomorphisms of an object in a bicategory, as... |
6,594 | lean_file_chunk | 6fdaac683bd7037c6338f81efd57e1839c727d9e53a1e0e2800bafa8936aa672 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Core
public import Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Pseudo
/-!
# (2,1)-categories
A bicategory `B`... |
3,118 | lean_file_chunk | f35329c2a4b4b7a070390da65f14fb8d5934077e104b1552268b60e4b542f6bc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Bicategory.End
public import Mathlib.CategoryTheory.Monoidal.Functor
/-!
# Promoting a monoidal category to a single object ... |
6,478 | lean_file_chunk | 540b623e3a4611fb715e096bd6d7cd8ede98dde848caefaa9057ee8190cfc303 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne
-/
module
public import Mathlib.CategoryTheory.Bicategory.Basic
public import Mathlib.CategoryTheory.Opposites
/-!
# Opposite bicategories
We construct the 1-cell opposite ... |
13,451 | lean_file_chunk | 70b973d8ab135c6643623e6ef098c458849e3e161ded9e0e81a91ff8b192ca70 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne, Joseph Hua
-/
module
public import Mathlib.CategoryTheory.Bicategory.LocallyDiscrete
public import Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Pseudo
/-!
# The ... |
4,244 | lean_file_chunk | 70cf08308c8bc8f686a44c3c1d0ffbb10044539c2c22f582adef3e678cda805c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
module
public import Mathlib.CategoryTheory.EqToHom
public import Mathlib.CategoryTheory.Bicategory.Basic
/-!
# `eqToHom` in bicategories
This file records some of t... |
12,970 | lean_file_chunk | c726be67bb0328d7055751a4ffe37a33eb78c6845ccb8d706e34b9cf01e0f998 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
module
public import Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor
/-!
# Free bicategories
We define the free bicategory over a quiver. In this bicategory, the... |
5,321 | lean_file_chunk | 8ca21bd885c9a6132861782973ce3ad36866f1763a430cdd3819776bdde3a9c2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno, Calle Sönne
-/
module
public import Mathlib.CategoryTheory.CommSq
public import Mathlib.CategoryTheory.Discrete.Basic
public import Mathlib.CategoryTheory.Bicategory.Strict.... |
5,399 | lean_file_chunk | 93d51a4ed5c2c7bbc14a0ab571b6edc80493f8a37d29bb009c4b4f2e0d54252b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne
-/
module
public import Mathlib.CategoryTheory.Bicategory.Functor.StrictPseudofunctor
/-!
# Induced bicategories
In this file we develop API for constructing a full sub-bi... |
15,369 | lean_file_chunk | fb116954267e0ad54ab7f9bccf8923a3280764096b4746d250ce4415bcf681de | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Emily Riehl
-/
module
public import Mathlib.CategoryTheory.Monoidal.Cartesian.Cat
public import Mathlib.CategoryTheory.Enriched.Basic
public import Mathlib.CategoryThe... |
18,537 | lean_file_chunk | b30319489b539c23c594931c65488d7d6a253bd8a2c925d5f183e2c3a46ef4ff | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers
public import Mathlib.CategoryTheory.Limits.Shapes.Reflexive
public import Mathlib.Categor... |
3,979 | lean_file_chunk | f08749a0be91bea68a87f279cd232bdbd14a246cf2efeaf7121e051ae4b17ef2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Comma.Over.Basic
public import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
public import Mathlib.CategoryTheory.Monad... |
13,700 | lean_file_chunk | d9b1dd93f1cfef7ee55c20cd515a852b8bdd6b9cbc40d53a6a8237f4800382fd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Bhavik Mehta, Adam Topaz
-/
module
public import Mathlib.CategoryTheory.Functor.Category
public import Mathlib.CategoryTheory.Functor.FullyFaithful
public import Mathlib.C... |
17,358 | lean_file_chunk | e677b2eb5cdd6795dcc399911d0054f8ac328c9f09ca454def335feb6ef2727d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jack McKoen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jack McKoen
-/
module
public import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers
public import Mathlib.CategoryTheory.Limits.Shapes.Reflexive
public import Mathlib.CategoryT... |
3,294 | lean_file_chunk | 70406ae37fb5daeb5fedb0005ecb33d2d0af0718e4e43d83a423480e1c777051 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
module
public import Mathlib.CategoryTheory.Monad.Basic
public import Mathlib.CategoryTheory.Monoidal.End
public import Mathlib.CategoryTheory.Monoidal.Mon_
/-!
# The equi... |
14,102 | lean_file_chunk | e2b142fc93b4294ac9094cc11bb9eae99f84add5af398ff9721516fc2acfcb7c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Adjunction.Reflective
public import Mathlib.CategoryTheory.Monad.Algebra
/-!
# Adjunctions and (co)monads
We ... |
2,201 | lean_file_chunk | 40485b36a9f434a02c6908788971c37935e5fd85b3f78db758f5d4fff8f15c0e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Category.KleisliCat
public import Mathlib.CategoryTheory.Monad.Basic
public import Mathlib.CategoryTheory.M... |
23,907 | lean_file_chunk | 90655c52f24dd6cd8b3f274a8114175a06560cb40ed3e51e5cb71b8aba5df51c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Bhavik Mehta, Jack McKoen
-/
module
public import Mathlib.CategoryTheory.Monad.Adjunction
public import Mathlib.CategoryTheory.Adjunction.Limits
public import Mathlib.Cate... |
6,000 | lean_file_chunk | 08d60017906a3aeb0eb283aa4e58f426a5def07ee650975eb13e29e8a40ef932 | lean_source_file | pkg_mathlib_source_file_chunks | instance comp_comparison_forget_hasColimit (F : J ⥤ D) (R : D ⥤ C) [ComonadicLeftAdjoint R]
[HasColimit (F ⋙ R)] :
HasColimit ((F ⋙ Comonad.comparison (comonadicAdjunction R)) ⋙ Comonad.forget _) := by
assumption
instance comp_comparison_hasColimit (F : J ⥤ D) (R : D ⥤ C) [ComonadicLeftAdjoint R]
[HasCol... |
13,193 | lean_file_chunk | 55c5519eced8a65696d1769db44e227080e6a037b5590f0accdc6b8b7fab9137 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Monad.Basic
public import Mathlib.CategoryTheory.Adjunction.Basic
public import Mathlib.CategoryTheory.Functor.... |
4,156 | lean_file_chunk | 821c8a2fe87f9d7bf794594cbcb6612187ffe7bd939d3885720effc23c608811 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Reflexive
public import Mathlib.CategoryTheory.Limits.Shapes.SplitCoequalizer
public import Mathlib.CategoryThe... |
4,206 | lean_file_chunk | 84b2d07c747193de8b692b94184bf3694eaef8bfbf6c695936258b76ef59069b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jack McKoen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jack McKoen
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Reflexive
public import Mathlib.CategoryTheory.Limits.Shapes.SplitEqualizer
public import Mathlib.CategoryTheory.... |
6,126 | lean_file_chunk | 65c52485dd941bd7d1daf6049e16e75331eeae45448d485f250d5d7fba9e0a54 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki, Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Adjunction.Basic
public import Mathlib.CategoryTheory.Monad.Basic
/-! # Kleisli category on a (co)mo... |
3,978 | lean_file_chunk | 1eb7b89d53f30bdcbdcf8818dd1d1512d4f8c719b160600f3abe8c9bbf6e711b | 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.Algebra.Homology.ShortComplex.Ab
public import Mathlib.CategoryTheory.Preadditive.Yoneda.Basic
public import Mathlib.CategoryTheory.Shift.ShiftedH... |
12,660 | lean_file_chunk | d374732b9923b22ef3cbfaa95795f2e9e7147816a6eca98d78fe52a380540f35 | 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.Algebra.Homology.ShortComplex.Exact
public import Mathlib.CategoryTheory.Shift.ShiftSequence
public import Mathlib.CategoryTheory.Triangulated.Fun... |
8,015 | lean_file_chunk | e480564c591326a84af4d8a8f7555db3a0e0fac752633085990be295e2ef6294 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 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.Linear.LinearFunctor
public import Mathlib.CategoryTheory.Triangulated.Rotate
public import Mathlib.Algebra.Ring.NegOnePow
/-!
# T... |
23,999 | lean_file_chunk | 10e7613f99e7956f06ecb8ea801abd5195d4fb6f6e1592069cd4d97c4f7a3f63 | 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.Localization.CalculusOfFractions
public import Mathlib.CategoryTheory.Localization.Triangulated
public import Mathlib.CategoryTheor... |
6,810 | lean_file_chunk | b9e3b16d2949d27943e23f9083ccfe45535702fcc63f7c96478e39f929156711 | lean_source_file | pkg_mathlib_source_file_chunks | exact ⟨MorphismProperty.LeftFraction.mk b s' ⟨_, _, _, mem', mem⟩, hb₁.symm⟩
ext := by
rintro X' X Y f₁ f₂ s ⟨Z, g, h, H, mem⟩ hf₁
have hf₂ : s ≫ (f₁ - f₂) = 0 := by rw [comp_sub, hf₁, sub_self]
obtain ⟨q, hq⟩ := Triangle.yoneda_exact₂ _ H _ hf₂
obtain ⟨Y', r, t, mem'⟩ := distinguished_cocone_triangle... |
15,349 | lean_file_chunk | f8baca017f56f2947a9a36c0d5aa48ab531def6f7d1f64f00374d212854a4545 | 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.Triangulated.Pretriangulated
/-!
# Triangulated Categories
This file contains the definition of triangulated categories, which ar... |
19,602 | lean_file_chunk | 8e29c30df961cdd52c43efb8717231f6fc390bd9760b6a75669ed3d15e28f979 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Luke Kershaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Luke Kershaw
-/
module
public import Mathlib.CategoryTheory.Adjunction.Limits
public import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products
public import Mathlib.CategoryTheory.... |
7,705 | lean_file_chunk | afbc1a98306ab411faf9b7ae76dff545bd93a42e10191422628182f52a9ed6d9 | 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.ComposableArrows.One
public import Mathlib.CategoryTheory.ComposableArrows.Two
public import Mathlib.CategoryTheory.Triangulated.Fu... |
8,711 | lean_file_chunk | 1ab5877a87edee1aa6f806dfe4ca5a5013e62c4d2e8ee4e0062d5971c38f1d1d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
module
public import Mathlib.CategoryTheory.ObjectProperty.ClosureShift
public import Mathlib.CategoryTheory.Triangulated.Subcategory
/-!
# Generators in triangul... |
16,432 | lean_file_chunk | 03bc28ccc20c35f8a148f413eb51e255aae87d94c81d6ab8f49869f32ae8b310 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 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.Triangulated.Triangulated
public import Mathlib.CategoryTheory.ComposableArrows.Basic
public import Mathlib.CategoryTheory.Shift.Co... |
5,423 | lean_file_chunk | c7b943cb66367a1c5eb5e93393a04dd61364897084516ae65fa479ae7b1496d0 | 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.ObjectProperty.Orthogonal
public import Mathlib.CategoryTheory.Triangulated.Subcategory
public import Mathlib.CategoryTheory.Object... |
10,024 | lean_file_chunk | 9b62af2d9e0508114f35890e720fb7b3c6b03c6596a1f107b9f679d299247918 | 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, Sophie Morel
-/
module
public import Mathlib.CategoryTheory.Triangulated.Functor
public import Mathlib.CategoryTheory.Shift.Adjunction
public import Mathlib.CategoryTheory.Adjun... |
23,966 | lean_file_chunk | be997ca0190028549072b8b9ce7e5a9e1d596a74756bbdb109d995c4d613c0fb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Luke Kershaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Luke Kershaw, Joël Riou
-/
module
public import Mathlib.Algebra.Homology.ShortComplex.Basic
public import Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts
publ... |
9,310 | lean_file_chunk | 9251da2eca56115772c380fe9d7cff4617b30bafa3795d2d02fcb92a6b9ee0c6 | lean_source_file | pkg_mathlib_source_file_chunks | set_option backward.isDefEq.respectTransparency false in
instance : HasBinaryBiproducts C := ⟨fun X₁ X₃ => by
obtain ⟨X₂, inl, snd, mem⟩ := distinguished_cocone_triangle₂ (0 : X₃ ⟶ X₁⟦(1 : ℤ)⟧)
obtain ⟨inr : X₃ ⟶ X₂, inr_snd : 𝟙 _ = inr ≫ snd⟩ :=
Triangle.coyoneda_exact₃ _ mem (𝟙 X₃) (by simp)
obtain ⟨fst :... |
4,226 | lean_file_chunk | 23b68cedba4a549b4e8f69b79d78edfaee3b2e4e2b4cd47e3cf848b221d9046a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Luke Kershaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Luke Kershaw
-/
module
public import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
public import Mathlib.CategoryTheory.Triangulated.Basic
/-!
# Rotate
This file adds the ability... |
6,171 | lean_file_chunk | 2a5b3cfb9e19c71a1c58efb6df48e86ed0cfc9b4dbd0c9f47fddcfe9a8d21763 | 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, Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Subobject.Lattice
public import Mathlib.CategoryTheory.ObjectProperty.ContainsZero
public import Mathlib.CategoryTheo... |
4,782 | lean_file_chunk | cbe4d6920ea0f9cec3f0c6565b37005e15d0c39f60b4bfd7efa63144c65ce241 | 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.Subobject.Lattice
public import Mathlib.CategoryTheory.ObjectProperty.ContainsZero
public import Mathlib.CategoryTheory.ObjectPrope... |
1,668 | lean_file_chunk | eeaa268029053425754e8247928021b0e0be4a609762eec3ccf62b444370c7ca | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Pablo Donato. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pablo Donato
-/
module
public import Mathlib.CategoryTheory.Subobject.Basic
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
/-!
# Subobjects presheaf
Following... |
3,285 | lean_file_chunk | 4a3608883c67b372f0b57769653a436a3ae5f44995154f72e4812015ac1f68de | 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: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Subobject.Basic
public import Mathlib.CategoryTheory.EssentiallySmall
/-!
# Well-powered categories
A category `(C : Type u... |
11,031 | lean_file_chunk | b9e5fa11b4b6be29a3835682c92a5c3519d4f2374e3b52b7bf73eb2c6362458b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.CategoryTheory.Subobject.WellPowered
public import Mathlib.CategoryTheory.Comma.LocallySmall
public import Mathlib.CategoryTheory.Limits.P... |
23,986 | lean_file_chunk | fef3c39d6124072d77e8f4c410e41d77c4201f035d30ceef2e70c83279f88cc9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Limits.Skeleton
public import Mathlib.CategoryTheory.Subobject.MonoOver
public import Mathlib.CategoryTheory.Sk... |
6,490 | lean_file_chunk | 13c12f4a072f60469b96d5c2b1521833cc2c6def2d059a4b0a85979390a5efa0 | lean_source_file | pkg_mathlib_source_file_chunks | /-- For any morphism `f : X ⟶ Y` and subobject `y` of `Y`, `Subobject.pullbackπ f y` is the first
projection in the following pullback square:
```
(Subobject.pullback f).obj y ----pullbackπ f y---> (y : C)
| |
((Subobject.pullback f).obj y).arrow ... |
7,613 | lean_file_chunk | bd2323bc1a87ba55feb6380403c9937916e1e827211ee5a452544cbefd48af1a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Subobject.Basic
public import Mathlib.CategoryTheory.Preadditive.Basic
/-!
# Factoring through subobjects
The... |
18,164 | lean_file_chunk | bfcf4bfd1bb2f5259876946a71aac2482ef9c5eafee57ee56c71ec2570488cbf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Comma.Over.Pullback
public import Mathlib.CategoryTheory.Adjunction.Reflective
public import Mathlib.CategoryTh... |
769 | lean_file_chunk | 7b5e83c405287f507d6bb488bb3b973b3e6e93ac1d89a6aef2413200d2bf47e2 | 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.Subobject.Basic
public import Mathlib.SetTheory.Cardinal.HasCardinalLT
/-!
# Cardinality of Subobject
If `X ⟶ Y` is a monomorphis... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.