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 |
|---|---|---|---|---|---|
2,625 | lean_file_chunk | eacc08f5ffadb900dc0e571a49c1af4c7ddd55abf73256566dec359e96bc6fe6 | lean_source_file | pkg_mathlib_source_file_chunks | CostructuredArrow (Functor.diag _) X ≌ CostructuredArrow (Over.forget X.2) X.1 :=
(ofDiagEquivalence X).trans <|
(ofCostructuredArrowProjEquivalence (𝟭 T) X.1 X.2).trans <|
CostructuredArrow.mapNatIso (Over.forget X.2).rightUnitor
section CommaFst
variable {C : Type u₃} [Category.{v₃} C] (F : C ⥤ T) (G : D... |
6,536 | lean_file_chunk | 103b0149d77e45b9b10f8ed3e2ef60571af4057aee638292b379864aa2b97004 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.Tactic.CategoryTheory.Reassoc
public import Mathlib.CategoryTheory.Comma.Over.Basic
/-!
# Typeclasses for `S`-objects and `S`-morphisms
**Wa... |
11,730 | lean_file_chunk | a6957cf258295351fc3a7b23eb15466e113db23d69ccebaf513748f5cb77fea1 | 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, Andrew Yang
-/
module
public import Mathlib.CategoryTheory.Adjunction.FullyFaithful
public import Mathlib.CategoryTheory.Adjunction.Mates
public import Mathlib.CategoryThe... |
2,604 | lean_file_chunk | 59b1c2fe16322166142381027edfee0783bae0047a41c2f359e841a63e616152 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Comma.Presheaf.Basic
public import Mathlib.CategoryTheory.Limits.Preserves.Yoneda
public import Mathlib.CategoryTheory.Limi... |
23,958 | lean_file_chunk | ffa5d9b0975e70ceef91f1d00c4c4d0dfa7997b8d39dc8754760ea7dfb5597be | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.HomCongr
public import Mathlib.CategoryTheory.Comma.Over.Basic
public import Mathlib.Tactic.CategoryTheory.Elementwise
/-!... |
6,472 | lean_file_chunk | f51a07ac290b7f6a6dbbc943cfa8d045966ffb740d393862056caa7ec4a142b0 | lean_source_file | pkg_mathlib_source_file_chunks | (s : CostructuredArrow yoneda A) : counitBackward F s ∘ counitForward F s = id :=
funext fun x => by simp [counitBackward]
/-- Intermediate stage of assembling the counit. -/
@[simps]
def counitAuxAux (F : (CostructuredArrow yoneda A)ᵒᵖ ⥤ Type v)
(s : CostructuredArrow yoneda A) :
F.obj (op s) ≅ OverArrows (... |
7,624 | lean_file_chunk | 32f161d4c5d4efb4537784b56ccc5f008138b6944696536a82b60514f138a573 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Sites.Coherent.ExtensiveTopology
public import Mathlib.CategoryTheory.Sites.Coherent.SheafComparison
public import Ma... |
13,355 | lean_file_chunk | 981d647b2c2dacd7bc0b05c81bfb653ebb143d52408a13bec49da70dd232e961 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Sites.Coherent.Comparison
public import Mathlib.CategoryTheory.Sites.Coherent.ExtensiveSheaves
public import Mathlib.... |
2,662 | lean_file_chunk | 7594df6ac1f2e3a4411739973e0d1a0901385050c10a193d8f1ebe5789dd3427 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Preadditive.Biproducts
public import Mathlib.CategoryTheory.Sites.Coherent.ExtensiveSheaves
public import Mathlib.Cat... |
5,427 | lean_file_chunk | 634d3118f2b6bd6cb8fb07d42bea71023f8dbe80fa7395813173ec9cc610edca | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Functor.OfSequence
public import Mathlib.CategoryTheory.Sites.Coherent.LocallySurjective
public import Mathlib.Catego... |
1,336 | lean_file_chunk | 262dabb99db5cddfe204527c294468e9c136bec2a201bcb4d00bb4894a21c563 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.EffectiveEpi.Enough
public import Mathlib.CategoryTheory.EffectiveEpi.Preserves
public import Mathlib.CategoryTheory.... |
4,800 | lean_file_chunk | c79bf4066bc299eb922960dccee10280b5c28f6f6a36847031e2d404c2f06940 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Nikolas Kuhn
-/
module
public import Mathlib.CategoryTheory.Sites.Coherent.CoherentSheaves
public import Mathlib.Data.Finite.Sigma
/-!
# Description of the covering sieves of... |
1,581 | lean_file_chunk | f11f3ac4a7572cafd733e6e9a76898ca81a227ae5478b9c746b932d4ca1a9d13 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.EffectiveEpi.Enough
public import Mathlib.CategoryTheory.EffectiveEpi.Preserves
public import Mathlib.CategoryTheory.... |
6,431 | lean_file_chunk | 92850cb48ff230f486e1a2f38d958d881b249744310f3dde64e7565fc1b379c1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Dagur Asgeirsson, Filippo A. E. Nuccio, Riccardo Brasca
-/
module
public import Mathlib.CategoryTheory.Extensive
public import Mathlib.CategoryTheory.Sites.Coverage
public imp... |
5,708 | lean_file_chunk | d420cd72632074fea8967a8f829466f02ac0c3cbb8cd78c6dba93c26d19a9adb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Filippo A. E. Nuccio, Riccardo Brasca
-/
module
public import Mathlib.CategoryTheory.Limits.Preserves.Finite
public import Mathlib.CategoryTheory.Sites.Canonical
p... |
2,506 | lean_file_chunk | 0752e10eaa9f3e2ce5885a853df9fff8344a121423b00696742146c90fdede0e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Sites.Coherent.Basic
public import Mathlib.Data.Finite.Sigma
/-!
# Description of the covering sieves of the extensi... |
2,518 | lean_file_chunk | 2873646b62184a5563b0d492c361bbf1a58c255afc04b7a3fc61110c8966a84e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 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.Sites.Canonical
public import Mathlib.CategoryTheory.Sites.Coherent.Basic
public import Mathlib.CategoryTheory.Sites.EffectiveEpi... |
4,251 | lean_file_chunk | 26ea9c9afa78702ef6fa01b9ba56e9b23255056b8d0e6a52d1f9633f339d428c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Sites.Coherent.SheafComparison
public import Mathlib.CategoryTheory.Sites.Equivalence
/-!
# Coherence and equivalenc... |
14,019 | lean_file_chunk | 2502a70ee5e2a7197b2890e2bd92190bc0251370618875ac98c2436cb25f18e2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Filippo A. E. Nuccio, Riccardo Brasca
-/
module
public import Mathlib.CategoryTheory.EffectiveEpi.Preserves
public import Mathlib.CategoryTheory.Limits.Final.Paral... |
4,362 | lean_file_chunk | 4e9b8bbd26a490911a45dc5c42f3380f9cd9995876582bc51795eaa20f16933b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 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.Sites.Coherent.Basic
public import Mathlib.CategoryTheory.EffectiveEpi.Comp
public import Mathlib.CategoryTheory.Effe... |
3,206 | lean_file_chunk | 74dfaf9a4b631b7731c6d2d387b61a09c3f4ceafb4be83ca472b902a36ba248b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 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.Sites.Coherent.RegularSheaves
/-!
# Description of the covering sieves of the regular topology
This file characteri... |
2,663 | lean_file_chunk | e8af9d413fa33bda57e8b2057fb39d48cc1cfacfa2961a473dab75addb469943 | 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.Sites.Point.Basic
/-!
# The category of points of a site
We define the category structure on the points of a site `(C, J)`:
a mor... |
2,871 | lean_file_chunk | d41e623e221cc7f9026badf2263450a3da67ab2c216086f4871c8400d7376d53 | 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, Christian Merten
-/
module
public import Mathlib.CategoryTheory.Sites.CoverPreserving
public import Mathlib.CategoryTheory.Sites.Point.Skyscraper
public import Mathlib.CategoryT... |
5,088 | lean_file_chunk | f327ed9c907c40d4e7492dd8379e17bc8b1f569d276405b587da93283f2f49c7 | 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.Localization.Monoidal.Functor
public import Mathlib.CategoryTheory.Monoidal.Limits.Colimits
public import Mathlib.CategoryTheory.Si... |
3,512 | lean_file_chunk | 11a47bb18b70397f7312edd4aa12fda62391bc3800c7fa6d2d611649eb19cbe5 | 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.Sites.Point.Conservative
/-!
# Points of presheaf toposes
Let `C` be a category. For the Grothendieck topology `⊥` on `C`, we kno... |
7,450 | lean_file_chunk | 37fc5070679edfcc2428e616899b68b3ae3320eeb2509be097842d726986a915 | 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.ShrinkYoneda
public import Mathlib.CategoryTheory.Sites.CoverLifting
public import Mathlib.CategoryTheory.Sites.Point.Basic
/-!
# ... |
3,563 | lean_file_chunk | c35fdb21d6b67fd3ff0569d3c71c5aa8c30cea6cb34b343a1ff10972a84fc810 | 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.Filtered.FinallySmall
public import Mathlib.CategoryTheory.Functor.TypeValuedFlat
public import Mathlib.CategoryTheory.Comma.Struct... |
6,498 | lean_file_chunk | 8f3ebd34eb4174dd796c487a24d4fcd13cb6d330bd498e033fc3af0c9790fd31 | 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.ShrinkYoneda
public import Mathlib.CategoryTheory.Sites.CoverLifting
public import Mathlib.CategoryTheory.Sites.Point.OfIsCofiltere... |
15,338 | lean_file_chunk | 8362d4b721677b30c5874900822ebc7238e1472df0b678eb4e512a9255c67c2b | 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.Abelian.GrothendieckAxioms.Types
public import Mathlib.CategoryTheory.Filtered.FinallySmall
public import Mathlib.CategoryTheory.Li... |
11,338 | lean_file_chunk | 9dd8e57b1c4cbe881ea75e58650ba38dde55cb94033ef5882bc24e6357fab005 | 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, Brian Nugent
-/
module
public import Mathlib.CategoryTheory.Sites.Point.Basic
/-!
# Skyscraper sheaves
Let `Φ` be a point of a site `(C, J)`. In this file, we construct the
sk... |
2,027 | lean_file_chunk | d460f358d90ad41e73e761b588f5a8a4e980d8cb87cbb0dac1f00c489763776d | 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.Sites.Point.Conservative
public import Mathlib.CategoryTheory.Sites.Point.Monoidal
/-!
# Monoidal structure on sheaves using enoug... |
11,703 | lean_file_chunk | 6baf088b53c1c190c71124f2c86144100826915eb8a948205d9a1311da80bd1b | 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.Sites.Point.Category
public import Mathlib.CategoryTheory.Sites.Point.Skyscraper
public import Mathlib.CategoryTheory.Abelian.Groth... |
23,953 | lean_file_chunk | 07b08f049a388a196707ee13ed25023c507b4889cf715ac3465bdfb1981b0fb6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Joël Riou
-/
module
public import Mathlib.CategoryTheory.Sites.Sheaf
public import Mathlib.CategoryTheory.Sites.CoverLifting
public import Mathlib.CategoryTheory.Sites.Cover... |
9,666 | lean_file_chunk | 7478f632618af854f69972cd336e0a1fac60d81d52e3f5495fc8630ad4d7d8d4 | lean_source_file | pkg_mathlib_source_file_chunks | lemma equalizer_mem {U V} (f₁ f₂ : U ⟶ V) (e : G.map f₁ = G.map f₂) :
Sieve.equalizer f₁ f₂ ∈ J _ :=
letI := IsDenseSubsite.isLocallyFaithful J K G
IsDenseSubsite.functorPushforward_mem_iff.mp (G.functorPushforward_equalizer_mem K f₁ f₂ e)
variable {J} (F : Sheaf J A)
lemma map_eq_of_eq {X Y : C} (f₁ f₂ : X ⟶... |
5,141 | lean_file_chunk | 05babefc2d143f8a465b0cbd3580274af178f82379f3ac5b9e8bcce41d36d799 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.CategoryTheory.Sites.DenseSubsite.Basic
/-!
# The equivalence of categories of sheaves of a dense subsite
If `G : C ⥤ D` exhibits `(C, J)` a... |
8,183 | lean_file_chunk | d981cab58359d9c068809fce09295f4d852ef4805827a4dabadc1dec7cb37e2e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.CategoryTheory.Sites.DenseSubsite.SheafEquiv
/-!
# Induced Topology
We say that a functor `G : C ⥤ (D, K)` is locally dense if for each cove... |
23,994 | lean_file_chunk | da6e4e055ef645dccc4bc14d996c030b5ad47dcbe249d916d056df021e83a4db | 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.Sites.DenseSubsite.Basic
/-!
# Equivalence of categories of sheaves with a dense subsite that is 1-hypercover dense
Let `F : C₀ ⥤... |
11,628 | lean_file_chunk | 277e384b8c857cf418722ffdc2ce317e71fe6fd7384e5772e06bccd82bfd94b1 | lean_source_file | pkg_mathlib_source_file_chunks | noncomputable def presheafMap {X Y : C} (f : X ⟶ Y) :
presheafObj data G₀ Y ⟶ presheafObj data G₀ X :=
Multiequalizer.lift _ _ (fun i₀ ↦ restriction data G₀ ((data X).f i₀ ≫ f)) (by
rintro ⟨⟨i₁, i₂⟩, j⟩
obtain ⟨a, h₁, h₂⟩ : ∃ a, a = F.map ((data X).p₁ j) ≫ (data X).f i₁ ≫ f ∧
a = F.map ((data X).p... |
3,730 | lean_file_chunk | e58d4b8d32b25aa8d0ecd4be7815967d771bf2fa2c21904e5dca14363efa71f5 | 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.Category.Grp.Abelian
public import Mathlib.Algebra.Category.Grp.Adjunctions
public import Mathlib.Algebra.Homology.DerivedCategory.Ext.Bas... |
2,476 | lean_file_chunk | 9abd4916e6f00ecb8971cf28b4e1caa196e984381016f0a40baf07888d45eba5 | 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.AlgebraicTopology.AlternatingFaceMapComplex
public import Mathlib.CategoryTheory.Limits.FormalCoproducts.Cech
/-!
# Cech cohomology
Given a fami... |
6,140 | lean_file_chunk | b10322edf24535460ed60fe2dba175c5b504bcfabc1265821af96cd104d718c7 | 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.DerivedCategory.Ext.ExactSequences
public import Mathlib.Algebra.Category.Grp.Biproducts
public import Mathlib.CategoryTheory.Sit... |
23,971 | lean_file_chunk | 6162529e7e2be389beef8fd268b22ff2890a52a613f4083112c817d4e6464c5e | 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, Christian Merten
-/
module
public import Mathlib.CategoryTheory.Sites.Descent.IsPrestack
/-!
# Descent data
In this file, given a pseudofunctor `F` from `LocallyDiscrete Cᵒᵖ` ... |
5,428 | lean_file_chunk | e756730e8e931abe5e896d503a4d5aefac6e41e91ccd1844d71a3c0eb139012d | lean_source_file | pkg_mathlib_source_file_chunks | structure IsStackFor (R : Presieve S) : Prop where
isEquivalence :
(F.toDescentData (fun (f : R.category) ↦ f.obj.hom)).IsEquivalence
variable {F} in
lemma IsStackFor.isPrestackFor {R : Presieve S} (h : F.IsStackFor R) :
F.IsPrestackFor R where
nonempty_fullyFaithful := ⟨by
rw [isStackFor_iff] at h
... |
3,173 | lean_file_chunk | aa064af3a2ae2764f3e2a01a0e66c4fb7d1dc4717917a8e971d5904e085b0bc7 | 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, Christian Merten
-/
module
public import Mathlib.CategoryTheory.Sites.Descent.DescentData
/-!
# Stacks: effectiveness of descent
Let `C` be a category with a Grothendieck topo... |
18,951 | lean_file_chunk | 48cc4ab77a30f96dfe8f9d084d48265356a013d799dbd4d73b4923b7aed88a2e | 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.Sites.Descent.IsStack
/-!
# Characterization of (pre)stacks for a precoverage
Let `F : LocallyDiscrete Cᵒᵖ ⥤ᵖ Cat` be a pseudofun... |
8,311 | lean_file_chunk | 6d6728d66da9e1cfd0655b53d12bcc4f4e31fe1ac51f9efde593ab207dbca4b5 | 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, Christian Merten
-/
module
public import Mathlib.CategoryTheory.Bicategory.Functor.Cat
public import Mathlib.CategoryTheory.Bicategory.LocallyDiscrete
public import Mathlib.Cate... |
8,082 | lean_file_chunk | 93072e22795ad5d9c6f3115bd9dad0944cfccb138d69fd2939b6817aa13ca1c7 | 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, Christian Merten
-/
module
public import Mathlib.CategoryTheory.Bicategory.Adjunction.Cat
public import Mathlib.CategoryTheory.Bicategory.LocallyDiscrete
public import Mathlib.C... |
13,761 | lean_file_chunk | eecc78ebf72d1003b495a4397e046fc8905d30b59138e6fca2fc3bef1633ee38 | 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, Christian Merten
-/
module
public import Mathlib.CategoryTheory.Sites.Descent.DescentData
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.ChosenPullback
/-!
# Desce... |
5,782 | lean_file_chunk | 8f72d7d7e1e51dda09bef24007d5b6fc65ae2e65f80c25badbbbd4a19a724413 | 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.Sites.Hypercover.One
/-!
# Characterization of sheaves using 1-hypercovers
In this file, given a Grothendieck topology `J` on a c... |
4,881 | lean_file_chunk | bcbf822711125b9fc8aba2112d02fb7b8ec66320656abe9ec5c8f615d5ffd00d | 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.Sites.Hypercover.Homotopy
public import Mathlib.CategoryTheory.Sites.Hypercover.SheafOfTypes
public import Mathlib.Ca... |
10,961 | lean_file_chunk | 4107fea23c915250019160bce18ec996e7d381d820b26da087f3836fc001d1d6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 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.Sites.Hypercover.One
public import Mathlib.CategoryTheory.Limits.Types.Multiequalizer
/-!
# `1`-hypercovers and (pr... |
5,667 | lean_file_chunk | d907a2eb34f1dcda1a88481dca993d4fbaf3c3e5dd2f775715dfa4f19d96ecbb | 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.Sites.Hypercover.Zero
/-!
# Defining precoverages via pre-`0`-hypercovers
A precoverage is a condition on all presi... |
5,411 | lean_file_chunk | 50d7b0ec50dfa8e2218d4dd48b5df82b5204f37cfc551394af569a8f0449bf28 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 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.Sites.Canonical
public import Mathlib.CategoryTheory.Sites.Hypercover.SheafOfTypes
public import Mathlib.CategoryTheo... |
23,915 | lean_file_chunk | d9777d2160be1b64e9672c33d594ab678a5ef3ef47babe39151818e7af2ca698 | 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.Limits.Shapes.Opposites.Products
public import Mathlib.CategoryTheory.Sites.Coverage
public import Mathlib.CategoryTheory.Sites.She... |
20,690 | lean_file_chunk | 6347a4ab488161acd7df546afb3d11630e4e801adc112c0309f6297ebb1ae195 | lean_source_file | pkg_mathlib_source_file_chunks | (F.congrIndexOneOfEqIso (congrFun hs₀.symm i) (congrFun hs₀.symm j) (g.s₁ k)).inv ≫
eqToHom (by rw [PreOneHypercover.congrIndexOneOfEq_congrFun hs₀ hs₁]) := by
refine ⟨fun h ↦ ?_, fun ⟨hs₀, hh₀, hs₁, hh₁⟩ ↦ Hom.ext' hs₀ hh₀ hs₁ hh₁⟩
subst h
simp [congrIndexOneOfEq]
section
variable (s₀ : E.I₀ ≃ F.I₀) ... |
23,971 | lean_file_chunk | fd5e293d80f1148684afa36743fc69a2137d5e6368b512762dc2b409f8a2cc74 | 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.Sites.Precoverage
public import Mathlib.CategoryTheory.Limits.Shapes.Products
/-!
# 0-hypercovers
Given a coverage ... |
9,351 | lean_file_chunk | 144cdadf1e102dc05b35b49bcc1fa1606f33e194ffc4639eca644643650a798b | lean_source_file | pkg_mathlib_source_file_chunks | ZeroHypercover.{max w w'} J T where
__ := E.toPreZeroHypercover.inter F.toPreZeroHypercover
mem₀ := by
rw [PreZeroHypercover.inter_def, PreZeroHypercover.presieve₀_reindex]
exact (E.bind (fun i ↦ F.pullback₁ (E.f i))).mem₀
/-- Replace the indexing type of a `0`-hypercover. -/
@[simps toPreZeroHypercover]
d... |
12,794 | lean_file_chunk | 0d53f5867109c0a03c2b763c17c89460bef62277643e9bc37227669de09ed4ef | 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.Quotient
public import Mathlib.CategoryTheory.Sites.Hypercover.One
public import Mathlib.CategoryTheory.Filtered.Basi... |
7,336 | lean_file_chunk | 330ebda738f88d6b695c215799089ec876bf05486e404006eaafb7258ee5139e | 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.Category.Grp.Basic
/-! The cohomology of a sheaf of groups in degree 1
In this file, we shall define the cohomology in degree 1 of a she... |
13,260 | lean_file_chunk | 406f5906eb6a2101081b6821ecfd90a5868d30272c74d369030c907c36a76b83 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Joël Riou
-/
module
public import Mathlib.Algebra.Homology.ExactSequence
public import Mathlib.CategoryTheory.Abelian.Refinements
/-!
# The four and five lemmas
Consid... |
7,244 | lean_file_chunk | 3ade7ec5fb692ec06467c200f0e1530a2849595cdcf2a0faa8198d19447bf3bf | 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.Algebra.Homology.ShortComplex.SnakeLemma
/-!
# Long exact sequence for the kernel and cokernel of a composition
If `f : X ⟶ Y` and `g : Y ⟶ Z` a... |
2,409 | lean_file_chunk | 69fd4a382a85b34a679603b9661f4a11ce0db8abd9575faa9404c8b0e3bf301b | 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.Abelian.Basic
public import Mathlib.CategoryTheory.ObjectProperty.ContainsZero
public import Mathlib.CategoryTheory.ObjectProperty.... |
23,977 | lean_file_chunk | 2363bb37369c42e9f9e451ea803cfc642cbcdfe43df5e798db79d5ad15316349 | 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.Abelian.SerreClass.MorphismProperty
public import Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive
public import... |
376 | lean_file_chunk | d2c279b0ee971155d8810f8fca0c1e65ce94e1e7a883ddfa8476b318cf379550 | lean_source_file | pkg_mathlib_source_file_chunks | exact MorphismProperty.IsInvertedBy.of_comp _ _ (Localization.inverts L _) _
· refine ⟨⟨Localization.lift F.obj hF L, ?_⟩,
⟨ObjectProperty.isoMk _ (Localization.fac F.obj hF L)⟩⟩
rw [← exactFunctor_comp_iff L P]
exact ObjectProperty.prop_of_iso _ (Localization.fac F.obj hF L).symm F.property
end SerreC... |
2,278 | lean_file_chunk | fb20a0653e7bb599410d141a05b6608b62b6f7d97090b0b9a1453bcb9c7e9555 | 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.Abelian.SerreClass.MorphismProperty
public import Mathlib.CategoryTheory.Localization.Bousfield
/-!
# Bousfield localizations with... |
7,987 | lean_file_chunk | e74617e9646bd3eec047915b90adae2a27954ccc9f181ceacb552979a92df3c4 | 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.Abelian.SerreClass.Basic
public import Mathlib.CategoryTheory.Abelian.CommSq
public import Mathlib.CategoryTheory.Abelian.DiagramLe... |
9,585 | lean_file_chunk | f70cd2f87343254f9492eb6438c23de1366aabf154514ce7b9c8b30487e0811a | 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.Abelian.GrothendieckCategory.Subobject
public import Mathlib.CategoryTheory.Limits.FunctorCategory.EpiMono
public import Mathlib.Ca... |
1,388 | lean_file_chunk | 45a74db2aa99b2dc735c6b5f099daaa0e97e929467216683e56f49c18f3ba8d5 | 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.Algebra.Homology.DerivedCategory.Ext.EnoughInjectives
public import Mathlib.CategoryTheory.Abelian.GrothendieckCategory.EnoughInjectives
/-!
# Ex... |
17,283 | lean_file_chunk | ea33436e2cba7b51a7b1e3fb00c7f41a3f4550a6de3e085a616056f7456c92ab | 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.Abelian.CommSq
public import Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ColimCoyoneda
public import Mathlib.CategoryTheory... |
845 | lean_file_chunk | ef7ee21ccbf6fe4dc0c916847062ec79c75500c2c1921e8d3ebd7759e8637ad9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.Abelian.GrothendieckCategory.EnoughInjectives
public import Mathlib.CategoryTheory.Generator.Abelian
/-!
# Grothendieck ca... |
4,570 | lean_file_chunk | 2f846e50bd952e3b337df13ffd7c520767d7b2af9a3a3d4894a9466bc993cd9b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Paul Reichert. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Reichert
-/
module
public import Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic
public import Mathlib.CategoryTheory.Abelian.Subobject
public import Mathlib.CategoryTheor... |
6,148 | lean_file_chunk | 6b3e1302069379b204f49f3104782485c2f3c51086a502847a9b9fd6e578bde2 | 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.Abelian.GrothendieckAxioms.Colim
public import Mathlib.CategoryTheory.Abelian.GrothendieckCategory.Basic
public import Mathlib.Cate... |
890 | lean_file_chunk | 0f7b7a49be295f4c79533d46a7e4e4282d5bb53d7bb978b4e6f217c185898c8b | 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.Abelian.GrothendieckCategory.Basic
public import Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Colim
public import Mathlib.Cate... |
1,388 | lean_file_chunk | 687acfeb8bcda2423ed81c49d4036be10e7c8bf4cea114bd9bd6d8870951cd5e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.Abelian.GrothendieckAxioms.FunctorCategory
public import Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Types
public imp... |
23,993 | lean_file_chunk | c324b90924057f90083cad7873e672c45456b09da7a4299986382ecf1dba93ae | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Isaac Hernando, Coleton Kotch, Adam Topaz
-/
module
public import Mathlib.Algebra.Homology.ShortComplex.ExactFunctor
public import Mathlib.CategoryTheory.Abelian.Functor... |
2,659 | lean_file_chunk | aa3ac2e17ab210905938acb082560a4e45b48c13511c425999197eb8ded86f9a | lean_source_file | pkg_mathlib_source_file_chunks | section EpiMono
open Functor
section
variable [HasZeroMorphisms C] [HasFiniteBiproducts C]
noncomputable instance hasExactColimitsOfShape_discrete_finite (J : Type*) [Finite J] :
HasExactColimitsOfShape (Discrete J) C where
preservesFiniteLimits := preservesFiniteLimits_of_natIso HasBiproductsOfShape.colimIso... |
3,304 | lean_file_chunk | 67bfe6bd14029afc4c1a3a6bd5be72cd8a349a1c43d058f9547b926c4233a516 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Joël Riou
-/
module
public import Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.FunctorCategory
public import Mathlib.CategoryTheory.Abelian.GrothendieckCatego... |
5,401 | lean_file_chunk | 2cfebce9e44eb90eb5a1fdd6910f419357f78de54e0f5867ddd0171ac236263e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.Abelian.GrothendieckAxioms.Basic
public import Mathlib.CategoryTheory.Limits.Connected
public import Mathlib.CategoryTheory... |
659 | lean_file_chunk | 3d400bba2dc67df591ea1298849cb01d3444ab5d6c6a46fb6364fbe0f6e327b8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.Limits.FilteredColimitCommutesFiniteLimit
public import Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic
/-!
# The ... |
1,017 | lean_file_chunk | 3590c686886bc6e2a24b067df6566ee8c8d70aab70623a8d36f0f0af54858424 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Abelian.GrothendieckAxioms.Basic
/-!
# AB axioms in functor categories
This file proves that, when the relevant lim... |
7,005 | lean_file_chunk | 991872ab1e30361b8065c102a19711f77b6454e0c0382318405a028bbfd60e0e | 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.Filtered.Final
public import Mathlib.CategoryTheory.Limits.Connected
public import Mathlib.CategoryTheory.MorphismProperty.Limits
p... |
8,014 | lean_file_chunk | 512d8a808ba864a81511653dcd05c8a4c2d1ab212720640ce5b2a01575f53fcc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Blake Farman. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Blake Farman
-/
module
public import Mathlib.CategoryTheory.Abelian.Preradical.Basic
public import Mathlib.CategoryTheory.Abelian.FunctorCategory
public import Mathlib.Algebra.Homology.... |
2,470 | lean_file_chunk | 224e26f6657bb8b2dc934a08e3c65b0804e605b55a48f3d79ac69e3edb1dd20a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Blake Farman. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Blake Farman
-/
module
public import Mathlib.CategoryTheory.Abelian.Basic
public import Mathlib.CategoryTheory.Subobject.MonoOver
public import Mathlib.CategoryTheory.Limits.FunctorCateg... |
2,634 | lean_file_chunk | 366e580034851019887f6e14d238df95571b2577115d2c5b52d9c60b7452e221 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Blake Farman. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Blake Farman
-/
module
public import Mathlib.CategoryTheory.Abelian.Preradical.Basic
public import Mathlib.CategoryTheory.Abelian.Preradical.Colon
public import Mathlib.CategoryTheory.A... |
1,952 | lean_file_chunk | b2c057c78d5e8e89d5858dea3f9fe5f214ada3ed9cee9f52f748a1951518cc72 | 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
-/
module
public import Mathlib.CategoryTheory.Abelian.Exact
public import Mathlib.CategoryTheory.Preadditive.Yoneda.Projective
public import Mathlib.CategoryTheory... |
11,896 | lean_file_chunk | ff14ef203c65435a245cb5fc3de52e8606a9a6ae40f4d816b5465ff3fc8b9a80 | 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.Algebra.Homology.DerivedCategory.Ext.TStructure
public import Mathlib.Algebra.Homology.DerivedCategory.KProjective
public import Mathlib.Algebra.H... |
13,107 | lean_file_chunk | e5a1a96f0b9bea25255b8b947c0953e5ca70dd35821cc925f880262a0ee7da9c | 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, Nailin Guan
-/
module
public import Mathlib.Algebra.Homology.DerivedCategory.Ext.EnoughInjectives
public import Mathlib.Algebra.Homology.DerivedCategory.Ext.EnoughProjectives
pu... |
4,330 | lean_file_chunk | 64dbfc3ffd5c327f6117c08d053368d84ceac565c03beaf69df0a309899e8a08 | 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.Algebra.Homology.Embedding.CochainComplex
public import Mathlib.CategoryTheory.Preadditive.Projective.Resolution
/-!
# Projective resolutions as ... |
14,566 | lean_file_chunk | b9c7b98a71372d96c92751564c3ef99fe50599d3a154df8ea39282150f838c61 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Kim Morrison, Jakob von Raumer, Joël Riou
-/
module
public import Mathlib.CategoryTheory.Preadditive.Projective.Resolution
public import Mathlib.Algebra.Homology.Homotopy... |
1,994 | lean_file_chunk | 673c2e1643a9fb7411dcd6f65b153a5756ca77504deea7dd8d970ea266d2db3d | 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
-/
module
public import Mathlib.CategoryTheory.Abelian.Exact
public import Mathlib.CategoryTheory.Preadditive.Injective.Basic
public import Mathlib.CategoryTheory.P... |
11,631 | lean_file_chunk | f91cb83b894191206360eee3a8fdad8117f9f3221abcc765d3e3adbeb554830a | 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.Algebra.Homology.DerivedCategory.Ext.TStructure
public import Mathlib.Algebra.Homology.DerivedCategory.KInjective
public import Mathlib.Algebra.Ho... |
12,487 | lean_file_chunk | 22b62b2d8c76bf7a3b6fa34c4d4ae4415b397df59353f7661c43aa70632f958d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Nailin Guan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nailin Guan
-/
module
public import Mathlib.Algebra.Homology.DerivedCategory.Ext.EnoughInjectives
public import Mathlib.Algebra.Homology.DerivedCategory.Ext.EnoughProjectives
public impo... |
4,407 | lean_file_chunk | bbd043547a614c276295c9a87c8a77e3b6b82389c6ab524f68430b40ed5e1867 | 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.Algebra.Homology.Embedding.CochainComplex
public import Mathlib.CategoryTheory.Preadditive.Injective.Resolution
/-!
# Injective resolutions as co... |
15,781 | lean_file_chunk | 4f4657de2362b460896521ef5eb8bad7e00670d09e2c18c418e1018311661bcd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Kim Morrison
-/
module
public import Mathlib.Algebra.Homology.HomotopyCategory
public import Mathlib.Algebra.Homology.ShortComplex.ShortExact
public import Mathlib.Categor... |
4,162 | lean_file_chunk | 6e3d69fda8e0dfc510a0b1d283eacbf35aae10f6f643f80851dd95f3b5de673a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.Abelian.Yoneda
public import Mathlib.CategoryTheory.Generator.Abelian
public import Mathlib.CategoryTheory.Abelian.Grothend... |
6,925 | lean_file_chunk | 14fcec446ceb3b2b5a0b8be8107a8c3374f60d7d8fb5cfc93635cb722a69c2ea | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.Algebra.Category.ModuleCat.Injective
public import Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Connected
public import Mathlib.Categ... |
12,972 | lean_file_chunk | b538711d7a81c65277412711c201ff62d338a285f3d1a3d5a71030fc13b9c936 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.Algebra.Category.Grp.Limits
public import Mathlib.CategoryTheory.Monoidal.Cartesian.Mon_
public import Mathlib.CategoryTheory.Monoidal.Grp_
/... |
1,001 | lean_file_chunk | c1c3609220bed97c3be548f4efc8eba32007b0a76a4c78515d77f55c95ce7c94 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Paul Lezeau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Lezeau
-/
module
public import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
public import Mathlib.CategoryTheory.Monoidal.Mod_
/-!
# Additional results about module objects in C... |
2,251 | lean_file_chunk | 7c6236c9a184c673e2dfc8184c8fa107f0e733d2770371c7313b0b09ebd34459 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Thomas Browning, Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Christian Merten
-/
module
public import Mathlib.Algebra.Group.Invertible.Basic
public import Mathlib.CategoryTheory.Limits.Preserves.FunctorCatego... |
12,895 | lean_file_chunk | 0c82e9c2335185ff66a6210f7a992b9fe21fc56982e45dfbd0190a77792fab67 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.CategoryTheory.Adjunction.Limits
public import Mathlib.CategoryTheory.Comma.Over.Pullback
public import Mathlib.CategoryTheory.Limits.Construc... |
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