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 |
|---|---|---|---|---|---|
2,297 | lean_file_chunk | 9855fc10283755a37b5e99ca5e7b9a1b0d0dc0cdcce58003bcbd5a25b07a4d63 | 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.WellPowered
public import Mathlib.CategoryTheory.Types.Basic
public import Mathlib.Data.Set.Subsingleton
/-!
# `Ty... |
18,587 | lean_file_chunk | e6968cd63b1cc82c5e5a3088014692aaf1e97e23d448f3dc5ef8e060a6ca36c8 | 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.Lattice
/-!
# Specific subobjects
We define `equalizerSubobject`, `kernelSubobject` and `imageSubob... |
23,961 | lean_file_chunk | cab3f72f3b66a3b78b781aa4dc48c52ffab3428988b128f3245d90d12ab5747b | 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.Functor.Currying
public import Mathlib.CategoryTheory.Subobject.FactorThru
public import Mathlib.CategoryTheory... |
1,464 | lean_file_chunk | 6da4a539fa2c8c9559a01e2833993fbdb58db435eb84086c9caa611735f44969 | lean_source_file | pkg_mathlib_source_file_chunks | exact mk_eq_mk_of_comm i (𝟙 X) e (by simp [e])
lemma subsingleton_of_isZero {X : C} (hX : IsZero X) : Subsingleton (Subobject X) :=
subsingleton_of_isInitial hX.isInitial
section ZeroObject
variable [HasZeroMorphisms C] [HasZeroObject C]
open ZeroObject
/-- A nonzero object has nontrivial subobject lattice. -/
... |
2,612 | lean_file_chunk | b2d7eac4b86272a5ceff9810f9cbaa45c0f35ac2babe08cd0f99909183d12ce4 | 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
-/
module
public import Mathlib.CategoryTheory.FinCategory.Basic
public import Mathlib.Data.Fintype.EquivFin
/-!
# Finite categories are equivalent to categories in `Type ... |
2,549 | lean_file_chunk | 542f2559049810e88cfc9a30dabc96a29de447c914f32b90d83a87adba872f42 | 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
-/
module
public import Mathlib.Data.Fintype.EquivFin
public import Mathlib.CategoryTheory.Discrete.Basic
public import Mathlib.CategoryTheory.Opposites
public import Mathl... |
5,134 | lean_file_chunk | f266f9aec2e959382c817f7967be177eff27f19600bc1a9aa888b22f254de0ce | 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.Adjunction.Basic
/-!
# Adjunctions with a parameter
Given bifunctors `F : C₁ ⥤ C₂ ⥤ C₃` and `G : C₁ᵒᵖ ⥤ C₃ ⥤ C₂`,
this file intro... |
23,950 | lean_file_chunk | 544d17fd953695bea89da130dd4b82168e400fb2523520b2ac2395f69ddb1b28 | 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, Emily Riehl, Joël Riou
-/
module
public import Mathlib.CategoryTheory.Adjunction.Basic
public import Mathlib.CategoryTheory.Functor.TwoSquare
public import Mathlib.Categor... |
1,151 | lean_file_chunk | 01922875c09627ea57cb03ce0ec40a20248ae7252457866d9b5b0bec2c8c789b | lean_source_file | pkg_mathlib_source_file_chunks | conjugateEquiv adj (adj.comp id) (rightUnitor L).hom =
(leftUnitor R).inv := by
cat_disch
lemma conjugateEquiv_whiskerLeft
{L₁ L₂ : B ⥤ C} {R₁ R₂ : C ⥤ B} {L : A ⥤ B} {R : B ⥤ A}
(adj₁ : L₁ ⊣ R₁) (adj₂ : L₂ ⊣ R₂) (adj : L ⊣ R) (τ : L₂ ⟶ L₁) :
conjugateEquiv (adj.comp adj₁) (adj.comp adj₂) (whiskerL... |
7,650 | lean_file_chunk | 26701cf6430719ef906f69c5e3b8f46e80b6a567435dde7351ab47463b4e3d78 | 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.Adjunction.Mates
/-!
# Compatibilities for left adjoints from compatibilities satisfied by right adjoints
In this file, given iso... |
10,578 | lean_file_chunk | 34c2a1c11702b621d798784a085d4e597b658c71387eb44c3c1a458275fc6820 | 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.Adjunction.FullyFaithful
public import Mathlib.CategoryTheory.Functor.EpiMono
public import Mathlib.CategoryTheory.HomCongr
... |
5,307 | lean_file_chunk | c7166a91f3d9735a41562fd90a74416ffc64bb49170780f81175b4877de6fb8b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Sophie Morel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sophie Morel, Joël Riou
-/
module
public import Mathlib.CategoryTheory.Preadditive.Yoneda.Basic
/-!
# Adjunctions between additive functors.
This provides some results and constructio... |
2,156 | lean_file_chunk | f953d5a68a9f2600d3c11705f140bf0264a922f40d7663d74427988d3499b599 | 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.Adjunction.FullyFaithful
public import Mathlib.CategoryTheory.Adjunction.Limits
/-!
# Preservation of colimits and reflective adju... |
7,433 | lean_file_chunk | 3b6b8d0df43cf144dcf6a420d61a9ad9184a0c21c91b27f2edb7dd6dd7d84680 | 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.StructuredArrow.Small
public import Mathlib.CategoryTheory.Generator.Basic
public import Mathlib.CategoryTheory.Limits.... |
6,460 | lean_file_chunk | 9ea1e5443f038605ef51d362bc18eea51fd97b2bf5834e387d4953e71a5bc63f | 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.Limits.Shapes.Terminal
public import Mathlib.CategoryTheory.Adjunction.Basic
public import Mathlib.CategoryTheory.Comma.Struc... |
4,154 | lean_file_chunk | f8a3cad77fbe8443d7c1e7fa95574c35c3b96bcf1dd674c98a18059efe1aa8e4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 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.Limits.Shapes.Products
public import Mathlib.CategoryTheory.Functor.EpiMono
/-!
# Adjunctions involving evaluation
We show tha... |
3,615 | lean_file_chunk | 9d7c35c03e8dcce0e447aa12cebbf1ca77d2669e682ae1663232255a168672f8 | 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
-/
module
public import Mathlib.CategoryTheory.Adjunction.Basic
public import Mathlib.CategoryTheory.HomCongr
/-!
# Restricting adjunctions
`Adjunction.restrictFullyFaith... |
23,999 | lean_file_chunk | 49f8ed43a1a61b3ffc1986b09e1bf10eb0a13d302b4aa1c963ff8809c3e64061 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Johan Commelin, Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Equivalence
public import Mathlib.CategoryTheory.Yoneda
/-!
# Adjunctions between functors
`F ⊣... |
9,041 | lean_file_chunk | 9a4a12a0c755c0c1f40c8bb233a0aef0ddb9b18f6da211662fc50d3660ab712a | lean_source_file | pkg_mathlib_source_file_chunks | uliftCoyoneda.{max w v₂} ⋙ (whiskeringLeft _ _ _).obj G :=
NatIso.ofComponents (fun X ↦ NatIso.ofComponents
(fun Y ↦ (Equiv.ulift.trans
((adj.homEquiv X.unop Y).trans Equiv.ulift.symm)).toIso))
section
variable {E : Type u₃} [ℰ : Category.{v₃} E] {H : D ⥤ E} {I : E ⥤ D}
(adj₁ : F ⊣ G) (adj₂ : H ⊣ I)
se... |
15,764 | lean_file_chunk | e16913c64b7252ba8d9df3640621ff36f3a30e39b5077b5c06936337503735e5 | 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.Adjunction.Basic
public import Mathlib.CategoryTheory.Limits.HasLimits
public import Mathlib.CategoryTheory.Yoneda
/-!
# Domain of... |
6,612 | lean_file_chunk | 6a83e393c9667bc4e692a140b62d547ddcd0b6e80b838edf8108c7c259f8ef0d | 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, Thomas Read, Andrew Yang, Dagur Asgeirsson, Joël Riou
-/
module
public import Mathlib.CategoryTheory.Adjunction.Mates
/-!
# Uniqueness of adjoints
This file shows that a... |
6,309 | lean_file_chunk | b5da9eb32ae1676d17966deb4344f4285c21ec82a5206bfb140d448c3d22bdc4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Ben Eltschig. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ben Eltschig
-/
module
public import Mathlib.CategoryTheory.Adjunction.Triple
public import Mathlib.CategoryTheory.Limits.FunctorCategory.EpiMono
/-!
# Adjoint quadruples
This file co... |
5,318 | lean_file_chunk | 7c2ddb2c75e43636c974fa5296553af2643a45ae07186017ee1a03405fba4770 | 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, Thomas Read, Andrew Yang
-/
module
public import Mathlib.CategoryTheory.Adjunction.Basic
public import Mathlib.CategoryTheory.Yoneda
public import Mathlib.CategoryTheory.O... |
12,478 | lean_file_chunk | e02443c406884eae717156bb01ff9c05ae74ae1b485ba5479326092ee1e53d14 | 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, Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Adjunction.Basic
public import Mathlib.CategoryTheory.MorphismProperty.Basic
public import Mathlib.Category... |
14,904 | lean_file_chunk | 85303e6673fc18b77eada44268b4f2d77f7bd78fd8741e57604ae0f60204248a | 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, Ben Eltschig
-/
module
public import Mathlib.CategoryTheory.Adjunction.Opposites
public import Mathlib.CategoryTheory.Adjunction.Unique
public import Mathlib.Categ... |
2,015 | lean_file_chunk | 10332961a48351cbab157e648bdbb89eb62b9eb9a600f64b9f59e06ad33f7a76 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 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.Whiskering
public import Mathlib.CategoryTheory.Adjunction.Basic
/-!
Given categories `C D E`, functors `F : D ⥤ E` and `G : E ... |
13,623 | lean_file_chunk | 3329edf27eb5eec520a667e47702d7fc16acd054de39b6419344ba3d3807d7ae | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Johan Commelin
-/
module
public import Mathlib.CategoryTheory.Adjunction.Basic
public import Mathlib.CategoryTheory.Limits.Creates
/-!
# Adjunctions and limits
A left adjo... |
2,318 | lean_file_chunk | 406e8bdf1bf094ed392ce0624333d22ee29da06e671c9a808a24a75ecbd1d1ea | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jacob Reinhold. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jacob Reinhold
-/
module
public import Mathlib.CategoryTheory.CopyDiscardCategory.Basic
public import Mathlib.CategoryTheory.Limits.Shapes.IsTerminal
/-!
# Markov Categories
Copy-di... |
1,530 | lean_file_chunk | 150cf2b747b76bffd203036cd3d2fe8083c645db8f0815afe68218fe3a9bcea2 | 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.LiftingProperties.Basic
public import Mathlib.CategoryTheory.Comma.Over.Basic
/-!
# Lifting properties in Over categories
In this... |
6,468 | lean_file_chunk | 72d4c0f5bec906a5655b7610d2008d8a04e6840101ca2fabc7968e3fcf30d443 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Jakob Scholbach. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob Scholbach, Joël Riou
-/
module
public import Mathlib.CategoryTheory.CommSq
public import Mathlib.CategoryTheory.Retract
/-!
# Lifting properties
This file defines the lifting... |
6,826 | lean_file_chunk | 1125084448c155895c96c8af591102055437effa74cbc39ebcb06a567e267768 | 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.LiftingProperties.Basic
public import Mathlib.CategoryTheory.Adjunction.Parametrized
public import Mathlib.CategoryTheory.Limits.Sh... |
4,985 | lean_file_chunk | d32151bc5f714dc6f0fb9bf3d3257a2ba16a120146cdb8e6ec8c527b99355b25 | 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.LiftingProperties.Basic
public import Mathlib.CategoryTheory.Adjunction.Basic
/-!
# Lifting properties and adjunction
In this fi... |
3,310 | lean_file_chunk | 779e31c3e854e1e0075dd444b56b048af002c3acd25ae4be3bbfc247755476c1 | 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.Products
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs
/-!
# Lifting properties an... |
15,605 | lean_file_chunk | 893eb54d971dda16d46cdb305c3c7222a2e673f41510223e4870f64e0416227a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joseph Hua. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Bhavik Mehta, Johan Commelin, Reid Barton, Robert Y. Lewis, Joseph Hua
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.IsTerminal
public import Mathlib.Category... |
23,994 | lean_file_chunk | f756c87d35cc4c0f2ac88f2af9922dca897c0c0fdc16c21dc266e4bad9909d2a | 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.Localization.Opposite
/-!
# Calculus of fractions
Following the definitions by [Gabriel and Zisman][gabriel-zisman-1967],
given a... |
14,905 | lean_file_chunk | 934413301a82ee186f67325a50e674e5bc1a005aa80e6c8135a2ad3f0996bfcc | lean_source_file | pkg_mathlib_source_file_chunks | rw [Q_map, Hom.map_mk, id_comp, comp_id, map_ofHom])
set_option backward.isDefEq.respectTransparency false in
lemma uniq (F₁ F₂ : Localization W ⥤ E) (h : Q W ⋙ F₁ = Q W ⋙ F₂) : F₁ = F₂ :=
Functor.ext (fun X => Functor.congr_obj h X) (by
rintro (X Y : C) f
obtain ⟨f, rfl⟩ := Hom.mk_surjective f
rw [show ... |
3,038 | lean_file_chunk | 8d6049b447c4eefded5b5a0631ed1be484a075f3055c2ad3d34532e18839eddb | 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.Localization.Equivalence
/-!
# Localization of the opposite category
If a functor `L : C ⥤ D` is a localization functor for `W :... |
3,214 | lean_file_chunk | b0d8cb7027ec45ddf44a0e01b9b5a2bafe26a1738e4cfe417011505b35f36df8 | 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.HasLocalization
public import Mathlib.CategoryTheory.EssentiallySmall
/-!
# Locally small localizations
In this file... |
296 | lean_file_chunk | 9a1544ab861a4431ad60b0196f06f74df2c97a0b679619ca5866798b31c00f85 | 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, Dagur Asgeirsson
-/
module -- shake: keep-all
public import Mathlib.CategoryTheory.Localization.Monoidal.Basic
deprecated_module (since := "2025-10-20") |
2,527 | lean_file_chunk | c14325010e4f5ba7d563f335b2397bfe4da71dacea5b141b9ad79c3069bb4756 | 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.Localization.Bousfield
public import Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition
public import Mathlib.CategoryT... |
13,714 | lean_file_chunk | 6dd73e1a526da0c172faef3a155256239e619fb46cb46f09dfd638ec16adc20b | 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.MorphismProperty.Composition
public import Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy
public import Mathlib.CategoryTheor... |
11,544 | lean_file_chunk | 055211fc89bbd1813bb75b2591a2c673e543f7b43042f46ee17e978b01a2f551 | 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.ComposableArrows
public import Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive... |
5,467 | lean_file_chunk | f23b6f3bf07e84db804419392825f278dca6f99696070f10e8d19bc5c308ccea | 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.Functor.Currying
public import Mathlib.CategoryTheory.Localization.Predicate
public import Mathlib.CategoryTheory.MorphismProperty.... |
5,760 | lean_file_chunk | baf3ed983eba400e62d71454604db8aee6e502849be38f72c159677d10451378 | 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.Localization.LocalizerMorphism
public import Mathlib.CategoryTheory.Functor.ReflectsIso.Basic
/-!
# Composition of localization fu... |
2,999 | lean_file_chunk | 8f7bde6176bfb176572cea7d78d7f59238b93be91c591f11a0c793daa90eb948 | 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.Localization.HasLocalization
public import Mathlib.CategoryTheory.Center.Localization
public import Mathlib.CategoryTheory.Center.L... |
1,117 | lean_file_chunk | 14b3047df4c8b9ab055ca481c2dc824309e2ceb6574ed7792137377957baa4b9 | 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.Localization.Predicate
public import Mathlib.CategoryTheory.Preadditive.FunctorCategory
/-!
# Localization of natural transformati... |
4,694 | lean_file_chunk | 3174f9beaf2283c64ef9a5633e8d19bc81a67831d3e189a6a7607eb361ec0b34 | 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.Localization.Prod
public import Mathlib.CategoryTheory.Localization.Equivalence
public import Mathlib.Data.Fintype.Option
/-!
# Lo... |
7,905 | lean_file_chunk | b709b341aeb3df88e17fe7f54f3b27a2e9f9dd404da40dc0e06104a37fb14ae4 | 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.Localization.Prod
public import Mathlib.CategoryTheory.Functor.Currying
/-!
# Lifting of bifunctors
In this file, in the context ... |
3,856 | lean_file_chunk | d5234f268b78075c71683eb28267538adc2ace1befb94f0687aa7c64f2660b8c | 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.Localization.LocalizerMorphism
public import Mathlib.CategoryTheory.Quotient
/-!
# Localization of quotient categories
Given a re... |
10,240 | lean_file_chunk | fc271bc6787a3e2ef3f13c731040c8c196a0485f788004d4c3d1d7a045e50e55 | 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.Localization.Bifunctor
public import Mathlib.CategoryTheory.Functor.CurryingThree
public import Mathlib.CategoryTheory.Products.Ass... |
10,299 | lean_file_chunk | 457c34d3f157eb9866c3acbae2c60f2f8aaf031806ebd823c5bcb7fd673b59c0 | 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.Localization.Equivalence
public import Mathlib.CategoryTheory.Localization.Opposite
/-!
# Morphisms of localizers
A morphism of l... |
11,033 | lean_file_chunk | 09884506f404fc7482a6733d114a6b74c1ce887264fd6af7f8d377a636842951 | 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.ObjectProperty.Local
public import Mathlib.CategoryTheory.MorphismProperty.Composition
public import Mathlib.CategoryTheory.Localiz... |
2,789 | lean_file_chunk | d9042f53f53f29c4462f7510674842bcc1f438c82c7aad5a9c9d0f341fe0f35e | 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.Localization.Predicate
/-! Morphism properties equipped with a localized category
If `C : Type u` is a category (with `[Category.... |
7,033 | lean_file_chunk | 0cb9a8cc6b3465339dccae611ce14cae6de63b773e1832a74aaf668a6ffc721e | 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.CatCommSq
public import Mathlib.CategoryTheory.Localization.Opposite
public import Mathlib.CategoryTheory.Adjunction.FullyFaithful
... |
15,664 | lean_file_chunk | 97be71e49f70fa39e15509cefef7cd253f759953a80012f6f1d814a64fc1b2ac | 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.HomEquiv
public import Mathlib.Logic.Small.Defs
/-!
# Shrinking morphisms in localized categories
Given a class of m... |
6,245 | lean_file_chunk | 3b612fd8ffe3c20338865aa46d673cb05a7d25329c3ad1f54d18e591ab94af1f | 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.LocalizerMorphism
public import Mathlib.CategoryTheory.HomCongr
/-!
# Bijections between morphisms in two localized c... |
4,873 | lean_file_chunk | a975e935fe67b0e6ae04f3f2c038d35790b258e4102f6d3ac10f8fc689f8ee4a | 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.ConeCategory
public import Mathlib.CategoryTheory.Limits.Preserves.Finite
public import Mathlib.CategoryTheory.Localization.... |
5,069 | lean_file_chunk | 3d7fb551f6519b184ad711b2a6b5f5ba4f1085a153cf196d1a6548ef40c45741 | 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.Localization.Predicate
public import Mathlib.CategoryTheory.CatCommSq
/-!
# Localization functors are preserved through equivalenc... |
20,497 | lean_file_chunk | 2bcc0bc5b0667f5f31e89e0b9e16e9229c900648e3e695de0f0d40acbc8ab317 | 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.SmallHom
public import Mathlib.CategoryTheory.Shift.ShiftedHom
public import Mathlib.CategoryTheory.Shift.Localization... |
5,080 | lean_file_chunk | 5a088eac6fd89e8e4919b4a50e665e8baec3cd76f6631cf7730e7d7e357fdf2f | 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.HomEquiv
public import Mathlib.CategoryTheory.Localization.Opposite
public import Mathlib.CategoryTheory.Comma.Structu... |
10,049 | lean_file_chunk | be22bd1a09b3cea5c78adff345843c27355f4a9063bd006cf953ab34b779c914 | 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.LocalizerMorphism
/-!
# Resolutions for a morphism of localizers
Given a morphism of localizers `Φ : LocalizerMorphi... |
22,204 | lean_file_chunk | 3fad08ed201a7b5ec690a7abca80695446c600dacc3843f2bfacfff9685fbc7e | 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.Localization.Construction
/-!
# Predicate for localized categories
In this file, a predicate `L.IsLocalization W` is introduced ... |
8,052 | lean_file_chunk | 59105ba48619a56abe5d86b7122d4b09cdc4c0ea0610c43873220d725bb76b71 | 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.Functor.KanExtension.Basic
public import Mathlib.CategoryTheory.Localization.Predicate
/-!
# Right derived functors
In this file,... |
7,821 | lean_file_chunk | 2d7f7b530d23b3f2f4a322c17ba98fe6d9c8277633d7f309f05e10accd0d2b47 | 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.Functor.KanExtension.Basic
public import Mathlib.CategoryTheory.Localization.Predicate
/-!
# Left derived functors
In this file, ... |
8,466 | lean_file_chunk | 31388634bd4bee5682be38c1d9bcf212dbe1bc1419252808e49269472e8d1bed | 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.Functor.Derived.RightDerived
public import Mathlib.CategoryTheory.Functor.KanExtension.Pointwise
public import Mathlib.CategoryTheo... |
6,301 | lean_file_chunk | 624fd04ba321f16171f2dc365c66c269b239909866cef9628bc59327246962f5 | 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.Functor.Derived.LeftDerived
public import Mathlib.CategoryTheory.Functor.Derived.RightDerived
/-!
# Derived adjunction
Assume tha... |
8,376 | lean_file_chunk | 6e65ccfe83ddc4ce84b254f08ac879707ce76e0311187bc3b0b28c1ce4c4b5a2 | 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.Functor.Derived.LeftDerived
public import Mathlib.CategoryTheory.Functor.KanExtension.Pointwise
public import Mathlib.CategoryTheor... |
6,022 | lean_file_chunk | e6ac65a0b21ec51e37641005c12e68aae3a7d593218009885386b718cf4495db | 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.Functor.KanExtension.DenseAt
public import Mathlib.CategoryTheory.Limits.Presheaf
public import Mathlib.CategoryTheory.Generator.St... |
23,942 | lean_file_chunk | 6f866e464d7eb476d30708bd606eb5f715b506371105138e66ac5c566be7dd79 | 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.Functor.KanExtension.Adjunction
public import Mathlib.CategoryTheory.Limits.Preserves.Basic
/-!
# Preservation of Kan exte... |
2,239 | lean_file_chunk | 804d4ccbd8986dd7c3eda69fc90f8e7fbfd42c65ba1e29d4471876d287f7ca00 | lean_source_file | pkg_mathlib_source_file_chunks | lemma pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac :
whiskerLeft L (pointwiseRightKanExtensionCompIsoOfPreserves G F L).inv ≫
(Functor.associator _ _ _).inv ≫ whiskerRight (L.pointwiseRightKanExtensionCounit F) G =
(L.pointwiseRightKanExtensionCounit <| F ⋙ G) := by
simp [pointwiseRightKanExtens... |
23,937 | lean_file_chunk | 3710bf8f887800437dbcb3e1e4b5b1fde4805df199a4b6b7c8f823fa1fd51aab | 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.Functor.KanExtension.Basic
/-!
# Pointwise Kan extensions
In this file, we define the notion of pointwise (left) Kan extension. G... |
7,207 | lean_file_chunk | 4917553d94889d34573c504203716ac7272c1b8cc328dadccc41eefa61123f3a | lean_source_file | pkg_mathlib_source_file_chunks | (LeftExtension.mk _ (pointwiseLeftKanExtensionUnit L F)).IsPointwiseLeftKanExtension :=
fun X => IsColimit.ofIsoColimit (colimit.isColimit _) (Cocone.ext (Iso.refl _) (fun j => by
dsimp
simp only [comp_id, colimit.ι_desc, CostructuredArrow.map_mk]
congr 1
rw [id_comp, ← CostructuredArrow.eq_mk]))
/--... |
23,976 | lean_file_chunk | 1ad6ffd168af653041a092ec94d5c525f951eb978f813fdf208247a3839d3e22 | 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.Comma.StructuredArrow.Basic
public import Mathlib.CategoryTheory.Limits.Shapes.Equivalence
public import Mathlib.CategoryTheory.Lim... |
13,425 | lean_file_chunk | be7b71b811b63969859dbd7e590fe5467e95e8241fd34902ed2b6fb7cb38a8df | lean_source_file | pkg_mathlib_source_file_chunks | lemma isLeftKanExtension_iff_of_iso₂ {F₁' F₂' : D ⥤ H} (α₁ : F₁ ⟶ L ⋙ F₁') (α₂ : F₂ ⟶ L ⋙ F₂')
(e : F₁ ≅ F₂) (e' : F₁' ≅ F₂') (h : α₁ ≫ whiskerLeft L e'.hom = e.hom ≫ α₂) :
F₁'.IsLeftKanExtension α₁ ↔ F₂'.IsLeftKanExtension α₂ := by
let eq := LeftExtension.isUniversalEquivOfIso₂ (LeftExtension.mk _ α₁)
(L... |
5,056 | lean_file_chunk | 5dec66b5c5af4e8d8166a4f907231ec6aadc1b447a527503a7fb13d3bd33cec5 | 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.Functor.KanExtension.Pointwise
public import Mathlib.CategoryTheory.Limits.Final
/-!
# Canonical colimits, or functors that are de... |
17,869 | lean_file_chunk | 03716741871e46ac22b60ac2c6a96472b71a77b23feba021aac0a0ff18fc3ca4 | 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.Functor.KanExtension.Pointwise
public import Mathlib.CategoryTheory.Limits.Shapes.Grothendieck
public import Mathlib.CategoryTheory... |
5,579 | lean_file_chunk | b1b31da1a37313f895bb7a0332fb01c272f9b740e83411d78d0ac60c219ba592 | 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.Limits.EpiMono
public import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers
public import Mathlib.Cate... |
1,509 | lean_file_chunk | 276b36964a8fe201441d297224564e27e6c43be1400ad8d3e4f6f1be24b1209c | 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: Bhavik Mehta, Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Functor.ReflectsIso.Basic
public import Mathlib.CategoryTheory.Balanced
public import Mathlib.CategoryTheory.... |
3,327 | lean_file_chunk | 4a805034089b3d838fadc0a54585f93a5a83bafffb36817b1f869f75932b830e | 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.Whiskering
public import Mathlib.CategoryTheory.Iso
public import Mathlib.CategoryTheory.Functor.FullyFaithful
/-!
# Functor... |
4,236 | lean_file_chunk | a4d63aa987decfba283a3a6baccfa51e86dc13d5e978407d6678d0345fd081a5 | 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.Functor.ReflectsIso.Jointly
public import Mathlib.Algebra.Homology.ShortComplex.Abelian
public import Mathlib.Algebra.Homology.Shor... |
2,958 | lean_file_chunk | c0b2d2632f4b482accc524627a2ee9fcd8de651533992c8e35b8dc09a2cf8ec3 | 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.Functor.ReflectsIso.Jointly
/-!
# Exactness of families of functors which jointly reflect isomorphisms
Let `Fᵢ : C ⥤ Dᵢ` be a con... |
5,663 | lean_file_chunk | f9c2a1d4e2192f030d52a4c2344af239318b6531482b563bebc0deda50772522 | 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.LimitsOfShape
public import Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic
/-!
# Preservation of limits, a... |
2,205 | lean_file_chunk | 751168d9fd34ff925ae5b8a6b5dae49358ecd111b251839516f8325a5095b1c0 | 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, Jonas van der Schaaf
-/
module
public import Mathlib.CategoryTheory.Monoidal.Closed.Basic
public import Mathlib.CategoryTheory.ObjectProperty.Retract
/-!
# Inter... |
2,926 | lean_file_chunk | 058877a77696969953289916bb214acabfa9146577636fbdc9ccd31d7c8cb256 | 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.Preadditive.Projective.Basic
/-!
# Preservation of projective objects
We define a typeclass `Functor.PreservesProjectiveO... |
1,847 | lean_file_chunk | e3a536443519b74ca2a4dc2f3c6bfc53c4509da485c493176445fb59f61d9a69 | 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.Preadditive.Projective.Basic
public import Mathlib.CategoryTheory.MorphismProperty.LiftingProperty
/-!
# Characterization of proje... |
9,688 | lean_file_chunk | 8528e711a2d00faa1386d589e47d18e576b1d0afb2ff29ac70226df26d975a22 | 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, Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Adjunction.FullyFaithful
public import Mathlib.CategoryTheory.Adjunction.Limits
public import Mathlib.Categor... |
6,498 | lean_file_chunk | 911bdd37b4593c6147d7ab3559c05c5e73defd61d44a5fbf29c708bfb827ee88 | 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, Joël Riou
-/
module
public import Mathlib.Algebra.Homology.QuasiIso
public import Mathlib.Algebra.Homology.SingleHomology
public import Mathlib.CategoryTheory.Preadditive.... |
2,870 | lean_file_chunk | 91c2718a5f877521306b22da00a5fcad01fe963dc904a5db5375f7aeeaec9b0b | 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.Preadditive.Injective.Basic
/-!
# Preservation of injective objects
We define a typeclass `Functor.PreservesInjectiveObje... |
1,843 | lean_file_chunk | aa63b2022f915f4d20ce87777d0d01970fab2243ae188201cd1849e24a606e55 | 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.Preadditive.Injective.Basic
public import Mathlib.CategoryTheory.MorphismProperty.LiftingProperty
/-!
# Characterization of inject... |
13,398 | lean_file_chunk | c0b84645a4d6b3d7c31924a89f137e0a28fd9d85a14108d50ed67bd196e3b8a4 | 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, Kevin Buzzard
-/
module
public import Mathlib.CategoryTheory.Preadditive.Projective.Basic
/-!
# Injective objects and categories with enough injectives
An object `J` is ... |
5,631 | lean_file_chunk | 25f4b69274f95d52e4a2e98e01e615abc8aef536addf51552ffbe899c6cc59ae | 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, Joël Riou
-/
module
public import Mathlib.Algebra.Homology.QuasiIso
public import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
public import Math... |
6,188 | lean_file_chunk | 83895c372eb638c544dc7ac01914b5550d1ad0244214735ceb0b83398da3d733 | 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.Preadditive.Opposite
public import Mathlib.Algebra.Category.ModuleCat.Basic
public import Mathlib.Algebra.Category.Grp.Prea... |
1,769 | lean_file_chunk | 09167e7b3369e53a40fd97ee2ebab3df30bd481e7bfaab689c2556acd3c538e9 | 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, Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Preadditive.Yoneda.Basic
public import Mathlib.CategoryTheory.Preadditive.Injective.Basic
public import Mathl... |
1,801 | lean_file_chunk | 0aed0d3fd8df7fe91381f69ab2fb25fffd1f9ec14a32335b0a6c5cf43aa85f1a | 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, Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Preadditive.Yoneda.Basic
public import Mathlib.CategoryTheory.Preadditive.Projective.Basic
public import Math... |
1,850 | lean_file_chunk | 93062b597005af4d3399b3f48949933f1af0d4a3d0e09e92119e0655d9a4903e | 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.Preadditive.Yoneda.Basic
public import Mathlib.Algebra.Category.ModuleCat.Abelian
public import Mathlib.CategoryTheory.Limi... |
1,205 | lean_file_chunk | 6586dfbc475f37df7bb2a63e450ba8f0f3d24b9f7fea831bf8f249c30a0db796 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Mario Carneiro and Emily Riehl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Emily Riehl
-/
module
public import Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction
public import Mathlib.CategoryTheory.Monad.Limits
/-!
# T... |
6,159 | lean_file_chunk | 2fa6c05be82628216a2083511f6f680366553c46fe2837e13e45c040c773f994 | 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.Category.Cat
public import Mathlib.CategoryTheory.Limits.Types.Limits
public import Mathlib.CategoryTheory.Limits.Preserves.B... |
919 | lean_file_chunk | 7d5c95bc8f728d339cefeca8ca06d40c1be95cffdaa58fc36a82807604fb0951 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Category.Cat
public import Mathlib.CategoryTheory.Category.ULift
/-!
# Functorially embedding `Cat` into the categor... |
2,231 | lean_file_chunk | 76016ab3d0ab1f85bbaa12305bda6a5c9edc685c621e5d92639cc983974ab088 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Emily Riehl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier, Emily Riehl
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Terminal
/-!
# Terminal categories
We prove that a category is terminal if its underlying type h... |
1,487 | lean_file_chunk | 147cce5faa137cd6921a308c65bda1df67af75cb04a374b468c863f9015c4116 | 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.Category.Cat
public import Mathlib.CategoryTheory.Opposites
/-!
# The dualizing functor on `Cat`
We define a (stric... |
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