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 |
|---|---|---|---|---|---|
1,711 | lean_file_chunk | 8c91bc70d7b5685b0d0654b65418438171f749ed3ec92917dbaae730247c955d | 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.Bicategory.Functor.LocallyDiscrete
public import Mathlib.CategoryTheory.Sites.Over
/-!
# Sheaves on Over categories, as a pseudofu... |
11,377 | lean_file_chunk | 6d1c12bd05aceabdcb11742354a8bb65fe21fc112f14bbb4230f9f471dfbe395 | 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.Sites.Grothendieck
public import Mathlib.CategoryTheory.Sites.Precoverage
/-!
# Grothendieck pretopologies
Definition and l... |
14,568 | lean_file_chunk | b55276c70fbd564e7a48bb9d9c8a1c7f1b8e5b77cb9c6eb6f76343ff0c0dfa14 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Limits.Types.Equalizers
public import Mathlib.CategoryTheory.Limits.Types.Products
public import Mathlib.CategoryTheory.Sites... |
1,383 | lean_file_chunk | 5e02caa13f66b25938a99a6dc75dc49c670e6b4d98f87bf604f24146e25585f5 | 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: Adam Topaz, Jujian Zhang
-/
module
public import Mathlib.CategoryTheory.Abelian.FunctorCategory
public import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
public import Mathlib.Ca... |
14,293 | lean_file_chunk | 8a97caef84c2cf8ce50e590c099238a767436bf9fd28c1139f430aaa3c9f160d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Benoît Guillemet. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Benoît Guillemet
-/
module
public import Mathlib.CategoryTheory.Sites.Hypercover.Zero
public import Mathlib.CategoryTheory.Sites.SheafOfTypes
/-!
# Grothendieck topolo... |
23,980 | lean_file_chunk | 1a1ab37a5b5f08166c7683116aaf0bcf8213a4e4c4dbffdbcf1c8345605b0fab | 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.Sites.Sieves
/-!
# The sheaf condition for a presieve
We define what it means for a presheaf `P : Cᵒᵖ ⥤ Type v` to be a she... |
21,624 | lean_file_chunk | e6967272ea9181fa5f4df3ff69e3ba2931cbcd7cf2e664622f8da4cc527da084 | lean_source_file | pkg_mathlib_source_file_chunks | simp [Equiv.subtypeEquiv]
/--
If `P` is a sheaf for the sieve `S` on `X`, a natural transformation from `S` (viewed as a functor)
to `P` can be (uniquely) extended to all of `yoneda.obj X`.
```
f
S → P
↓ ↗
yX
```
-/
noncomputable def IsSheafFor.extend {P : Cᵒᵖ ⥤ Type v₁} (h : IsSheafFor P (S : Presie... |
6,799 | lean_file_chunk | 3872e290445857f413086b213925e719f5ccd376f7cd3998617423f76c9441dd | 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.Limits.Preserves.Shapes.Products
public import Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products
public import ... |
14,273 | lean_file_chunk | d36a4cbf196ca2ebce5729f769f1e8aa24f1808dae350340dc0522c3d543a2b3 | 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.Limits.Preserves.Creates.Pullbacks
public import Mathlib.CategoryTheory.Sites.Sieves
public import Mathlib.Order.Cond... |
19,317 | lean_file_chunk | c0d35439f1b45fec41196905f356084cf6916629407ab92f1cde2f982c5d13d1 | 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.Sites.Equivalence
public import Mathlib.CategoryTheory.Limits.Constructions.Over.Connected
public import Mathlib.CategoryTheory.Lim... |
3,608 | lean_file_chunk | f71f7645cf58cbdaa6e134b8d7d6c5039023e71ec4dee8195395678784ed6eae | 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.DenseSubsite.Basic
public import Mathlib.CategoryTheory.Sites.LocallySurjective
/-!
# Preserving and reflectin... |
9,285 | lean_file_chunk | 07cb58ce4308f7d56cbb11309020a86b323f41079f72532f1d5d80776ea10df9 | 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.Sites.Over
/-! Internal hom of sheaves
In this file, given two sheaves `F` and `G` on a site `(C, J)` with values
in a category `... |
16,669 | lean_file_chunk | 644266da86eb3f0664ba1bacdd478dbc5faab9409b383bca176f35b7593763cf | 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.Adjunction.Restrict
public import Mathlib.CategoryTheory.Functor.KanExtension.Adjunction
public import Mathlib.Categ... |
5,329 | lean_file_chunk | daedf6061d6a5130d6a9ae11eb00a9fdf4fc259f8427f778d28430c9552db653 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.EffectiveEpi.Comp
public import Mathlib.CategoryTheory.Functor.RegularEpi
public import Mathlib.CategoryTheory.Limits... |
10,504 | lean_file_chunk | 47498ee7cb3635c0987591287b42a08b333184dbd3b1e72c18fba4c15a8843c7 | 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.Sites.Pretopology
public import Mathlib.CategoryTheory.Sites.IsSheafFor
/-!
# Sheaves of types on a Grothendieck topology
D... |
3,356 | lean_file_chunk | c8a32f31377ad02231f55cab94849e70e506c3cf11b1a407d96f2d2eccfb68ee | 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.Sites.Grothendieck
public import Mathlib.CategoryTheory.Sites.Pretopology
public import Mathlib.CategoryTheory.Limits.Lattice... |
23,961 | lean_file_chunk | cbca0cb27fdcd3ea137532b747efbc837a54670c68f7b940f1c81d6a2499cf3c | 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, Edward Ayers
-/
module
public import Mathlib.Data.Set.BooleanAlgebra
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs
public import Mathlib.Cate... |
23,900 | lean_file_chunk | d0ad8e35f6eb7f603bd9e5f3aea63c33c9c2d7f32c6b7e00560492eb36537947 | lean_source_file | pkg_mathlib_source_file_chunks | ⟨fun H _ _ hg => H _ ⟨_, 𝟙 _, _, hg, id_comp _⟩, fun ss Y f => by
rintro ⟨Z, f, g, hg, rfl⟩
exact S.downward_closed (ss Z _ hg) f⟩
/-- Show that there is a Galois insertion (generate, underlying presieve). -/
def giGenerate : GaloisInsertion (generate : Presieve X → Sieve X) arrows where
gc := generate_le_i... |
3,428 | lean_file_chunk | 45da32f4a775607b3c0ece00999a5e2aeb248e8cabe4adf75df2b007ef0336aa | lean_source_file | pkg_mathlib_source_file_chunks | instance uliftFunctorInclusion_top_isIso : IsIso (Sieve.uliftFunctorInclusion.{w} (⊤ : Sieve X)) :=
⟨⟨{ app := fun _ ↦ TypeCat.ofHom fun a ↦ ⟨a.down, ⟨⟩⟩ }, rfl, rfl⟩⟩
lemma ofArrows_eq_pullback_of_isPullback {ι : Type*} {S : C} {X : ι → C} (f : (i : ι) → X i ⟶ S)
{Y : C} {g : Y ⟶ S} {P : ι → C} {p₁ : (i : ι) → ... |
11,297 | lean_file_chunk | 03516fb3215193123865e06fd2974cc40b849f75ec9c9c18cf2126afaaff87f0 | 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.Sites.Sheaf
/-!
# The plus construction for presheaves.
This file contains the construction of `P⁺`, for a presheaf `P : Cᵒᵖ ⥤... |
9,483 | lean_file_chunk | 573ad2759811645c87de89b6db4487aab6621932840f9590efb8763cc11fa56e | 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.LeftExact
public import Mathlib.CategoryTheory.Sites.PreservesSheafification
public import Mathlib.CategoryTheory.Sites.Subsh... |
7,980 | lean_file_chunk | ae5c66a30907f0fb7c20e5ffced0674b85bcb201fdfbb0fac06ac9581fe5fa11 | 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.Sites.Whiskering
public import Mathlib.CategoryTheory.Sites.Plus
/-!
In this file, we prove that the plus functor is compatible... |
2,707 | lean_file_chunk | 7cc38ebedb23329b471fea9e612ff46e99d44741082dd90c0c8a1fe2ff0c0bdf | 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.Over
/-!
# Topology on `Over X` is subcanonical if the ba... |
4,109 | lean_file_chunk | a3e74c71bc8dfad8a61ce01147359611a7ded79547f7e99dfe82576a22328c95 | 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.Bousfield
public import Mathlib.CategoryTheory.Sites.Sheafification
/-!
# The sheaf category as a localized category
... |
10,103 | lean_file_chunk | 946a11a98fe91bd4d7c7c95e91ab16147745850d763c025e75eb666fd4c67041 | 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.Adjunction.Unique
public import Mathlib.CategoryTheory.Adjunction.Reflective
public import Mathlib.CategoryTheory.Sit... |
1,085 | lean_file_chunk | 9a826f3891102c2c280129b8004ee0e1c9da3890fc82ce0f2450bc23363e7893 | 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.Monoidal.Closed.Ideal
public import Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory
public import Mathlib.C... |
10,185 | lean_file_chunk | 4ff6ed3e8f624fcea398c16a3839261077bc22f2513e6f47db102b9a295dbb08 | 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.Sheafification
public import Mathlib.CategoryTheory.Sites.DenseSubsite.SheafEquiv
/-!
# The constant sheaf
We... |
4,564 | lean_file_chunk | 1f0e8e1db89ffac67aed48026968ee4a8baba654934616d341fa8bbacb111ee0 | 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.Adjunction.Restrict
public import Mathlib.CategoryTheory.Functor.Flat
public import Mathlib.CategoryTheory.Sites.Continuous
pub... |
6,091 | lean_file_chunk | f97bbdef663b342f9db21e8428c6569554ae1907a373086378e122a3feec6939 | 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.Sites.Sheaf
/-! Objects which cover the terminal object
In this file, given a site `(C, J)`, we introduce the notion of a family
... |
3,223 | lean_file_chunk | d403f53f8fc56a970d5b26d9401195d42a0d3027ab9674542719e7f81058d5c5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Jonas van der Schaaf. 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.Sites.Canonical
public import Mathlib.CategoryTheory.Sites.Subcanonical
public import Mathl... |
5,157 | lean_file_chunk | 30e156a011c1229af6c867de4d34de0d31c189acd1d79f105b6ae405c37edd3e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.CategoryTheory.MorphismProperty.Limits
public import Mathlib.CategoryTheory.Sites.Pretopology
public import Mathlib.CategoryTheory.S... |
4,747 | lean_file_chunk | cf92a90533b69c301d27b4207486be4127fb688d269b7c058cb5cbca7259f115 | 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, Joël Riou
-/
module
public import Mathlib.CategoryTheory.Adjunction.Restrict
public import Mathlib.CategoryTheory.Adjunction.Whiskering
public import Mathlib.CategoryTheory.Si... |
16,388 | lean_file_chunk | 3d0caaebcba8e15bf20899476fe339930ddd3748b01999005ab16dd4f6d14650 | 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, Andrew Yang
-/
module
public import Mathlib.CategoryTheory.Sites.Closed
public import Mathlib.CategoryTheory.Sites.Localization
public import Mathlib.CategoryTheory.Sites.Hyperc... |
12,340 | lean_file_chunk | 76ae60836dec806c7dc0ff76fba5f5bafe26ae73abbc092cc3263ebae0806173 | 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.Localization
public import Mathlib.CategoryTheory.Sites.CompatibleSheafification
public import Mathlib.CategoryTheory.Sites.W... |
23,995 | lean_file_chunk | 6ce8a8558a84d7e4cfc8fa699a26343858f9b94770aa1bf7c6ee72e5520817e4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kevin Buzzard, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers
public import Mathlib.CategoryTheory.Limits.Preserves.Shapes... |
7,393 | lean_file_chunk | 6a37424f8f86c925bf8737faa2f194a665bc8f82b2232b6f0eeee2fd1749198c | lean_source_file | pkg_mathlib_source_file_chunks | apply hh.uniq K
rintro (a | b)
· apply he
· rw [← K.w (WalkingMulticospan.Hom.fst b), ←
(T.multifork P).w (WalkingMulticospan.Hom.fst b), ← assoc]
congr 1
apply he
variable {J P} in
/-- If `F : Cᵒᵖ ⥤ A` is a sheaf for a Grothendieck topology `J` on `C`,
and `S` is a cover of `X : C`, th... |
23,972 | lean_file_chunk | 9773788818565169d092a17b0eae21274b3d2119e745e50054c492801e8a2ab9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Bhavik Mehta, Edward Ayers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Edward Ayers
-/
module
public import Mathlib.CategoryTheory.Sites.Sieves
public import Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
public import Math... |
1,086 | lean_file_chunk | 2047f710038cd28da76b913c3d32e476bf690f3b087b0720ba83b7fa5d47cd96 | lean_source_file | pkg_mathlib_source_file_chunks | noncomputable abbrev toMultiequalizer {D : Type u₁} [Category.{v₁} D] (S : J.Cover X)
(P : Cᵒᵖ ⥤ D) [Limits.HasMultiequalizer (S.index P)] :
P.obj (Opposite.op X) ⟶ Limits.multiequalizer (S.index P) :=
Limits.Multiequalizer.lift _ _ (fun I => P.map I.f.op)
(by
intro I
dsimp only [shape, index,... |
8,405 | lean_file_chunk | cfe90cb4a4e39ee409367b0c2bb819ecc23b2b7332a88653347d0bf21acc8936 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
module
public import Mathlib.CategoryTheory.Sites.Canonical
/-!
# Grothendieck Topology and Sheaves on the Category of Types
In this file we define a Grothendieck topology o... |
6,715 | lean_file_chunk | 71bf7180d4540687f25d8adc5c8d65ad4e671653ca0a08ed1b065b14e57c37c6 | 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.Sites.Sheaf
public import Mathlib.CategoryTheory.ConcreteCategory.Forget
/-!
In this file we construct the functor `Sheaf J A ⥤... |
9,534 | lean_file_chunk | df122353ab00dcd521d53346fc503b62b2c5de1ccff70a92d910330fa4d9c9f3 | 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.Creates
public import Mathlib.CategoryTheory.Sites.Sheafification
public import Mathlib.CategoryTheory.Limits.Shapes.Finit... |
11,881 | lean_file_chunk | 9e9b017b2f64c3195a24e9496e4917743e9174ba8a36e9d2b27050cf18578efe | 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.Sites.SheafOfTypes
public import Mathlib.Order.Closure
public import Mathlib.CategoryTheory.Subfunctor.Basic
/-!
# Closed si... |
16,573 | lean_file_chunk | ed3587759591a4c0b47403417f7b1f5956cd2826ad5cf8e31b0897dc0a39148e | 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.Limits.Preserves.Ulift
public import Mathlib.CategoryTheory.Sites.Canonical
public import Mathlib.CategoryTheory.Site... |
11,000 | lean_file_chunk | e47d6a0130a4e9b2d750ad42b3c9c2026d5b6b2611f1d82bfa096880fabbc3be | 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.ShortComplex.ShortExact... |
13,135 | lean_file_chunk | f8ce97943212d5a25d6ce842940de3029c5a7be913170904e73ec2ffdccff44c | 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.DenseSubsite.InducedTopology
public import Mathlib.CategoryTheory.Sites.LocallyBijective
public import Mathlib.... |
5,811 | lean_file_chunk | 7644e1191dc11a30ad11bee7e74a2d95aa441780b471e4116cf6b6250ac0248e | 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.Sites.CompatiblePlus
public import Mathlib.CategoryTheory.Sites.ConcreteSheafification
/-!
In this file, we prove that sheafifi... |
23,289 | lean_file_chunk | 74a0b8a5e9e275f796a974298535718d72a31cca8b109a6aa68f0e58a7bd30c5 | 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.Sites.Plus
public import Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory
/-!
# Sheafification
We construct the sheafific... |
2,650 | lean_file_chunk | a709ac694c1fbce75a97b0f0ca82c712b0430a9d96b1a85dfa8a5804a529bc1d | 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.Grp.Abelian
public import Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four
public import Mathlib.CategoryTheory.Abelian.... |
7,777 | lean_file_chunk | d45e069210c3dca4ee7b0ed3866cc5a678c28e5895a0fb999213672d2215a067 | 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.ModuleEmbedding.Opposite
public import Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Indiz... |
5,584 | lean_file_chunk | e703d44e1dfbfe802ade57d96b302773c9c8586a4109948d3a30869e985a1d91 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Abelian.Basic
public import Mathlib.CategoryTheory.Preadditive.Opposite
public import Mathlib.CategoryTheory.Limits.Opposites... |
18,173 | lean_file_chunk | 63cb50d1765619548a5c494ec2d1e383bd6f1a165c39a6c0b1a4cd94044d297b | 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.Additive
public import Mathlib.CategoryTheory.Abelian.Injective.Resolution
/-!
# Right-derived fu... |
2,628 | lean_file_chunk | 19ec2a5d0f7e2395fde14017b997ec093593fc9f113cc093707f2122ce705c95 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
module
public import Mathlib.CategoryTheory.ObjectProperty.FiniteProducts
public import Mathlib.CategoryTheory.ObjectProperty.Kernels
/-!
# Subcategories of abeli... |
1,392 | lean_file_chunk | a2f57d8df13b58abfe5bbb3e538233b7eae9460f7fdfd27c874c03fa6da514de | 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.Indization
public import Mathlib.CategoryTheory.Abelian.FunctorCategory
public import Mathlib.CategoryTheory.Li... |
19,831 | lean_file_chunk | 0639dd9d44c0dc4077705e1b23f6a1a75a3ae3087914403ea9e03bcd99ca4c14 | 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
-/
module
public import Mathlib.CategoryTheory.Abelian.Exact
public import Mathlib.CategoryTheory.Comma.Over.Basic
public import Mathlib.Algebra.Category.ModuleCat.EpiMon... |
23,986 | lean_file_chunk | de333d3aa81f90e6859cab394695f4e7e58bd4d3431b6e41856ee71602728c3a | 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, Johan Commelin, Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Limits.Constructions.Pullbacks
public import Mathlib.CategoryTheory.Preadditive.Biproducts
pu... |
13,569 | lean_file_chunk | 34f4e4323d78543d4e57eddbef0cf4ed291a773145ab25c8a1e82e27c774f755 | lean_source_file | pkg_mathlib_source_file_chunks | def isLimitPullbackToBiproduct : IsLimit (pullbackToBiproductFork f g) :=
Fork.IsLimit.mk _
(fun s =>
pullback.lift (Fork.ι s ≫ biprod.fst) (Fork.ι s ≫ biprod.snd) <|
sub_eq_zero.1 <| by
rw [Category.assoc, Category.assoc, ← comp_sub, sub_eq_add_neg, ← comp_neg, ←
biprod.desc_e... |
18,054 | lean_file_chunk | 88311e996f183b14801ef6233d0e8bfef6e223efe3c902aafba78d83eb892843 | 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, Riccardo Brasca, Adam Topaz, Jujian Zhang, Joël Riou
-/
module
public import Mathlib.Algebra.Homology.Additive
public import Mathlib.CategoryTheory.Abelian.Projective.Reso... |
2,981 | lean_file_chunk | 60029ccc0c221a36cff10649f9af2644a44288245f9cdc47be561fe274f88db0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.CategoryTheory.Subobject.Limits
public import Mathlib.CategoryTheory.Abelian.Basic
/-!
# Equivalence between subobjects and quotients in ... |
3,051 | lean_file_chunk | e2dc94aa5e4a8f00397bc7aca425b10d2cf8fb298b746d8f72d739066703a128 | 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, Adam Topaz
-/
module
public import Mathlib.Algebra.Category.ModuleCat.Abelian
public import Mathlib.Algebra.Homology.Opposite
public import Mathlib.CategoryTheory.Abelian.... |
11,823 | lean_file_chunk | 99f9b5da224fd2785d748f7bebdeeafe83cb3deb9adc526daee2aead34e32e4d | 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.Algebra.Homology.ShortComplex.Exact
/-!
# Refinements
In order to prove injectivity/surjectivity/exactness properties for diagrams
in the catego... |
1,232 | lean_file_chunk | 7cd054c4e429faf9c7d3bb8bfec54bfd19c13539c54b429e9561516752c0d1fd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Paul Lezeau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Lezeau, Edison Xie
-/
module
public import Mathlib.Algebra.Homology.ShortComplex.ShortExact
public import Mathlib.CategoryTheory.Abelian.Exact
/-! # Short Exact Sequences in Abeli... |
12,592 | lean_file_chunk | faa497ae254bc7254dd282ad6dcac971f3745cd2455de9c44b2d5c4f9252a31d | 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, Adam Topaz, Johan Commelin, Jakob von Raumer
-/
module
public import Mathlib.Algebra.Homology.ImageToKernel
public import Mathlib.Algebra.Homology.ShortComplex.Exact
pub... |
996 | lean_file_chunk | 4acd3c1c6f3bfacccf14669a22ef75df15024a2abb7e6894198c36392c80d11d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.MorphismProperty.Limits
public import Mathlib.CategoryTheory.Abelian.Basic
/-!
# Monomorphisms are stable under cobase change
In ... |
6,575 | lean_file_chunk | ae46864155f5587100947ce365fd002ae0b6c33cf088a321d3ecbd0681c5f8fc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Abelian.Basic
public import Mathlib.CategoryTheory.Adjunction.Limits
public import Mathlib.CategoryTheory.Limits.Preserves.Sh... |
3,460 | lean_file_chunk | 451fb52412eaa134c698427c97618744b993b6734c4122c9a64e27178595ae81 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.Algebra.Homology.ShortComplex.ShortExact
public import Mathlib.CategoryTheory.MorphismProperty.Composition
/-!
# Epimorphisms with an injective k... |
4,424 | lean_file_chunk | 0a2ae85be208c2cfda5bc02fb753cec120047db2f33e616e0db251027b520acf | 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.Limits.Shapes.Kernels
/-!
# The abelian image and coimage.
In an abelian category we usually want the image... |
3,391 | lean_file_chunk | 8a1043f9fb357f2802bfe2f885f84c19f1109e673a3e195a39196e6fbd24aaed | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Abelian.Basic
public import Mathlib.CategoryTheory.Preadditive.FunctorCategory
public import Mathlib.CategoryTheory.Limits.Fu... |
17,096 | lean_file_chunk | 7e213e13c216e7c44709d3b2297813ade0f5c1ed557f827f1e146eecf6cecbde | 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
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts
public import Mathlib.CategoryTheory.Limits.Shapes.Kernels
public import Mathlib.CategoryTheor... |
5,343 | lean_file_chunk | 11564d3234a5f51b608cdfd6ccdc3e51a1c2fa3103f3cf1cb24141fe277d48a0 | 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.Refinements
public import Mathlib.CategoryTheory.MorphismProperty.Limits
public import Mathlib.Algebra.Homology.CommSq
/-!... |
7,940 | lean_file_chunk | fdec2f24575bde5134fbdb7da07d5e54401b7b8e17daf5aa36e63b6e59048042 | 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.Adjunction.FullyFaithful
public import Mathlib.CategoryTheory.Monoidal.Functor
public import Mathlib.CategoryTheory.ObjectPro... |
9,202 | lean_file_chunk | 6e280e4ed96925cc612d70d141fc546ca535c4756e43b9ca10baf4cfe9245ce9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Monoidal.NaturalTransformation
/-!
# Transport a monoidal structure along an equivalence.
When `C` and `D` are equivalent a... |
15,957 | lean_file_chunk | cd2548e696f255c56519c91d575a917de97c1394ced12e2fe2c875197e33818c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Monoidal.Functor
public import Mathlib.Tactic.CategoryTheory.Monoidal.PureCoherence
public import Mathlib.Tactic.CategoryTheo... |
23,956 | lean_file_chunk | 979139fcb9f1a569a72ad32428c7193d277d2f542d205004ad4e84ddc5f175d5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Michael Jendrusch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Kim Morrison, Bhavik Mehta, Jakob von Raumer
-/
module
public import Mathlib.CategoryTheory.EqToHom
public import Mathlib.CategoryTheory.Functor.Trifunctor
publi... |
14,372 | lean_file_chunk | 295d2e6859691a3f2e55c96eb5616295a40ac9d16c36f3dd10c6c4325876366a | lean_source_file | pkg_mathlib_source_file_chunks | (α_ (W ⊗ X) Y Z).inv ≫ (α_ W X Y).hom ▷ Z ≫ (α_ W (X ⊗ Y) Z).hom =
(α_ W X (Y ⊗ Z)).hom ≫ W ◁ (α_ X Y Z).inv :=
eq_of_inv_eq_inv (by simp)
@[reassoc (attr := simp)]
theorem pentagon_hom_inv_inv_inv_inv :
W ◁ (α_ X Y Z).hom ≫ (α_ W X (Y ⊗ Z)).inv ≫ (α_ (W ⊗ X) Y Z).inv =
(α_ W (X ⊗ Y) Z).inv ≫ (α_ W X... |
4,033 | lean_file_chunk | 66833d64eaff23f70f9bfdca2501eb17905c2311da92dd9d3d287e060bde0e88 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Algebra.Group.Hom.Defs
public import Mathlib.CategoryTheory.Discrete.Basic
public import Mathlib.CategoryTheory.Monoidal.NaturalTransformati... |
23,974 | lean_file_chunk | 4d0a5dc18e8c3159e4e2b2467a1ee993db746281d15eef452f71a8b7626fbe38 | 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.Monoidal.Cartesian.Mon_
public import Mathlib.CategoryTheory.Limits.ExactFunctor
public import Mathlib.CategoryTheory.Limit... |
6,844 | lean_file_chunk | 7f21c0fd12269642483eb77b3a4ee4385a2af24cd70e479339f82da7b6d3070a | lean_source_file | pkg_mathlib_source_file_chunks | /-- A finite-product-preserving functor takes group objects to group objects. -/
@[to_additive (attr := simps!)
/-- A finite-product-preserving functor takes additive group objects to additive group objects. -/]
def mapGrp : Grp C ⥤ Grp D where
obj A := .mk (F.obj A.X)
map f := Grp.homMk' (F.mapMon.map f.hom)
@[to... |
6,579 | lean_file_chunk | 48b7b268554b24212939ba234db1391c485f2b5858a4acfa94db6d4e13beac7c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Antoine Labelle. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle
-/
module
public import Mathlib.CategoryTheory.Monoidal.Braided.Basic
public import Mathlib.CategoryTheory.Monoidal.Linear
public import Mathlib.CategoryTheory.Monoid... |
1,478 | lean_file_chunk | 9631a16558283a3f6fef446100c11ce89ef0391eeccb636830ddd496e42391a9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Lean FRO LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Monoidal.Comon_
/-!
# The convolution monoid.
When `M : Comon C` and `N : Mon C`, the morphisms `M.X ⟶ N.X` form a monoid (... |
5,005 | lean_file_chunk | 653fc6a9fd1c6c82684adf00dc1a867292b30ae6aced6ca9d80612fcbb979579 | 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.Algebra.Group.Equiv.Defs
public import Mathlib.CategoryTheory.Monoidal.Braided.Basic
public import Mathlib.CategoryTheory.Monoidal.Transport... |
12,364 | lean_file_chunk | 52925ee5f7b57232b00fbe501a0fd05f3a5e1ee1ed3e1b56dea3180507c2def2 | 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, Simon Hudon
-/
module
public import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
public import Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts
public impo... |
7,834 | lean_file_chunk | e2e312209f37e9594b3e2e2ab11eefb04acd71d3806fe329b8e7e5777b3a7635 | 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, Paul Lezeau, Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Monoidal.Mon_
public import Mathlib.CategoryTheory.Monoidal.Action.Basic
/-!
# The category of m... |
23,961 | lean_file_chunk | a52bb52c5152f8a19801befb46eebaacf657cc57c4f0da2950fc7c1c4d5282ab | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Oleksandr Manzyuk
-/
module
public import Mathlib.CategoryTheory.Bicategory.Basic
public import Mathlib.CategoryTheory.Monoidal.Mon_
public import Mathlib.CategoryTheory.L... |
17,256 | lean_file_chunk | 4c13319e7ea06b5ed1bbf2cd6441b3221382e5f429280f7d84ed88c68234a38f | lean_source_file | pkg_mathlib_source_file_chunks | /-- The underlying morphism of the inverse component of the left unitor isomorphism. -/
noncomputable def inv : P.X ⟶ TensorBimod.X (regular R) P :=
(λ_ P.X).inv ≫ (η[R.X] ▷ _) ≫ coequalizer.π _ _
theorem hom_inv_id : hom P ≫ inv P = 𝟙 _ := by
dsimp only [hom, inv, TensorBimod.X]
ext; dsimp
slice_lhs 1 2 => r... |
2,230 | lean_file_chunk | ac056b89d5136c187b37f9199483d6269a90255495a7d9c48c7119a729d49d24 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Linear.LinearFunctor
public import Mathlib.CategoryTheory.Monoidal.Preadditive
/-!
# Linear monoidal categories
A monoidal ... |
15,763 | lean_file_chunk | 0faee86f2f77dbfee77a3071568a58ee48f7af0b4f88f3a1a517c6542247228f | 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.Preadditive.AdditiveFunctor
public import Mathlib.CategoryTheory.Monoidal.Functor
/-!
# Preadditive monoidal categories
A m... |
9,293 | lean_file_chunk | f934be2258ef501d09c80439f89918a79e74bc6edb8373806a3f0dc66611bcf8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Jack McKoen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jack McKoen
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj
public impor... |
13,221 | lean_file_chunk | c27e3787377282d1cb1b716525aff78e826c872690bcae399cb536a44455b174 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Monoidal.Braided.Basic
public import Mathlib.CategoryTheory.Functor.ReflectsIso.Basic
/-!
# Half braidings and the Drinfeld ... |
10,237 | lean_file_chunk | 04c641f9add19d856626aea46d5767288d1e04f09f86979f1abc26a1c7be1d57 | 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.Monoidal.Grp_
public import Mathlib.CategoryTheory.Monoidal.CommMon_
/-!
# The category of commutative groups in a Cartesi... |
12,116 | lean_file_chunk | 62605ae44e6684204522168d5e4230819f94f9a11f9b3a35e7fe9e73cb550104 | 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, Andrew Yang
-/
module
public import Mathlib.CategoryTheory.Monoidal.Functor
/-!
# Endofunctors as a monoidal category.
We give the monoidal category structure on `C ⥤ C`... |
2,528 | lean_file_chunk | a7a22e5ba1c29f7e22ac83ec8e1dd194af2c04f999823812c00dc97437512876 | 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.Monoidal.Comon_
public import Mathlib.CategoryTheory.Monoidal.Braided.Basic
public import Mathlib.CategoryTheory.Monoidal... |
2,183 | lean_file_chunk | 0e69148ef4dfc0657a83c315b0a5710f82c726184bc090b02dd747de5fc4820e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Michael Jendrusch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Kim Morrison, Bhavik Mehta, Jakob von Raumer
-/
module
public import Mathlib.Tactic.CategoryTheory.Monoidal.PureCoherence
/-!
# Lemmas which are consequences of... |
23,990 | lean_file_chunk | ffb5847d8691504868bdd65be1d8f5d109d47ef6ff54d398637ac278c1d858c7 | 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.Monoidal.ExternalProduct.KanExtension
public import Mathlib.CategoryTheory.Products.Associator
/-!
# Day convolution monoi... |
23,915 | lean_file_chunk | dda1f8609c77ff828f70d1f44c2d19c9f18a5531b8408e7f60bc9f937e7a4f09 | lean_source_file | pkg_mathlib_source_file_chunks | isoWhiskerLeft _ (isoWhiskerLeft _
(NatIso.ofComponents fun _ ↦ Equiv.toIso <|
(prod.rightUnitorEquivalence C).congrLeft.fullyFaithfulFunctor.homEquiv))
_ ≅ (whiskeringLeft _ _ _).obj
((prod.rightUnitorEquivalence C).inverse ⋙
((𝟭 C).prod (Functor.fromPUnit.{0} (𝟙_ C)))... |
15,072 | lean_file_chunk | 14c9252669a558523d945097550fa720bab54473d099430a51a651a32a777ddd | lean_source_file | pkg_mathlib_source_file_chunks | core data needed to construct a full `LawfulDayConvolutionMonoidalCategoryStructCore`.
We are making this a class so that it can act as a "proxy" for inferring `DayConvolution`
instances (which is all the more important that we are modifying the instances given in the
constructor to get better ones defeq-wise). As this... |
14,046 | lean_file_chunk | 0b3cff1f3d87ac83b44494b0c8aaf3007ec95df983978107510687915add1591 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Lean FRO LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Monoidal.Bimon_
public import Mathlib.CategoryTheory.Monoidal.Conv
/-!
# The category of Hopf monoids in a braided monoidal ... |
11,751 | lean_file_chunk | e4ace49aa01b7c3feca105f0f1bc088696abdfac4861152aac58dff40630c487 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Monoidal.Braided.Basic
public import Mathlib.CategoryTheory.Monoidal.Mon_
/-!
# The category of commutative monoids in a bra... |
23,974 | lean_file_chunk | 071783e3e073162535fd6b5db2bf2af1422d8cc9a397280c45c9f01cc3d8a3ae | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Michael Jendrusch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Kim Morrison, Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Monoidal.Category
public import Mathlib.CategoryTheory.Adjunction.FullyFaithful
public ... |
23,961 | lean_file_chunk | 3539d30932a553bf9255af2a8db6e730e880a22dc5c669ff6c69b7c154f5383a | lean_source_file | pkg_mathlib_source_file_chunks | @[simps -isSimp, implicit_reducible]
def toOplaxMonoidal : F.OplaxMonoidal where
η := h.εIso.inv
δ X Y := (h.μIso X Y).inv
δ_natural_left _ _ := by
rw [← cancel_epi (h.μIso _ _).hom, Iso.hom_inv_id_assoc,
← h.μIso_hom_natural_left_assoc, Iso.hom_inv_id, comp_id]
δ_natural_right _ _ := by
rw [← can... |
5,584 | lean_file_chunk | 4b38c5738dc23fd8770de75d6d1ef44464a337b3116cf110cf57a87022a8bae7 | lean_source_file | pkg_mathlib_source_file_chunks | /-- The composition of two monoidal category equivalences is monoidal. -/
instance isMonoidal_trans [e'.functor.Monoidal] [e'.inverse.Monoidal] [e'.IsMonoidal] :
(e.trans e').IsMonoidal := by
dsimp [Equivalence.IsMonoidal]
rw [trans_toAdjunction]
infer_instance
end
end Equivalence
variable (C D)
/-- Bundl... |
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