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 |
|---|---|---|---|---|---|
12,525 | lean_file_chunk | ef389572d41b999c4ba52b08028657cd595a01badb3fe71c3ccfddea6fcdaa2a | lean_source_file | pkg_mathlib_source_file_chunks | coprod.map (F.map f) (F.map g) ≫ coprodComparison F A' B' := by
rw [coprodComparison, coprodComparison, coprod.map_desc, ← F.map_comp, ← F.map_comp,
coprod.desc_comp, ← F.map_comp, coprod.inl_map, ← F.map_comp, coprod.inr_map]
/-- The coproduct comparison morphism from `FA ⨿ F-` to `F(A ⨿ -)`, whose components a... |
10,597 | lean_file_chunk | ba6a36964749e74d492f5ee20be34bd48a9150114b02d1811c2817a0862bd5ba | 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, Christian Merten
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
p... |
14,933 | lean_file_chunk | 9a58cc4808dd77f5a8af174ae99d8dfd5985a4b6c58309e3a0b7dfb41a19a744 | 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, Kim Morrison, Adam Topaz
-/
module
public import Mathlib.CategoryTheory.ConcreteCategory.EpiMono
public import Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic
public import... |
3,006 | lean_file_chunk | 77450e33a2975dec88026dbb2deaaf4e5ffadb546527d7ec61e619b9b6bdbc70 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.CategoryTheory.FinCategory.Basic
public import Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
public import Mathlib.Data.Fintype.Sum
publ... |
10,566 | lean_file_chunk | 5f979560f53c08f96aa54d312752b556834b93dbd57165088ec9c2b42a8440c1 | 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.Final
public import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts
public import Mathlib.CategoryTheory.C... |
1,738 | lean_file_chunk | 733694342ef418f3f992faf4cf34aad13eb7df2ee97d25e6536cf5a009018c35 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 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.Types.Filtered
public import Mathlib.CategoryTheory.ConcreteCategory.Forget
public import Mathlib.CategoryTheo... |
3,180 | lean_file_chunk | 1cb2a263fcc82b68b7aa44cbd296cb9559bed646cba70ef2eb095e030d5ab5fe | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
module
public import Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic
public import Mathlib.Algebra.Category.ModuleCat.Basic
public import Mathlib.Tactic.CategoryThe... |
7,456 | lean_file_chunk | 4d08b5a04596422777cde004b177dac82f4b21a08a720498eaa9ff8a54f9c8cf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 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.CategoryTheory.ConcreteCategory.Forget
public import Mathlib.CategoryTheory.Limits.Preserves.Basic
public import Mathlib.Categor... |
4,021 | lean_file_chunk | a6d6c5cda2ba609fc4cde046f37c90917cb399fccd90fe457bcc5963698f01f4 | 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.Limits.Final
/-!
# Action of an initial functor on sections
Given `F : C ⥤ D` and `P : D ⥤ Type w`, we define a map
`sectionsPrec... |
2,254 | lean_file_chunk | 58c191f1aa48d80f7cb4226f21766d03319ee71174133ca5727065a3658e2d26 | 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.Limits.Final
public import Mathlib.CategoryTheory.Discrete.StructuredArrow
/-!
# Characterization of connected categories using in... |
2,122 | lean_file_chunk | 1e05f5f93058c0351f37e9e6116b75f91cfe1f014699f327976f4b7cb64310c4 | 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, Joël Riou
-/
module
public import Mathlib.CategoryTheory.Limits.Final
/-!
# Conditions for `parallelPair` to be initial
In this file we give sufficient condition... |
3,746 | lean_file_chunk | 9164c050a3652c83e3c1694ba1809d25b896de14a416a248433907b93c1accd8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.CategoryTheory.Limits.Preserves.Ulift
public import Mathlib.CategoryTheory.Limits.FunctorToTypes
/-!
# Yoneda preserves certain colimits
... |
16,319 | lean_file_chunk | 0a60bbe56265c01f0f20db7051edee440e2ea2d90c0f7d87be3bc34f467c5e31 | 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.Limits.Preserves.Basic
public import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts
/-!
# Preservation of finite (co)limi... |
12,144 | lean_file_chunk | 173a21f8cf4c3e49f15fcd419ca7d0fbb1de2386edb00bf8e27b5cd128df4f68 | 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, Justus Springer
-/
module
public import Mathlib.CategoryTheory.Limits.Preserves.Basic
public import Mathlib.CategoryTheory.Filtered.Basic
/-!
# Preservation of filtered c... |
9,689 | lean_file_chunk | 3dd53fefbe7007d637385c87aab796f2dc8584cbb0ff3e063c19f293d23dce8d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.CategoryTheory.Limits.FilteredColimitCommutesFiniteLimit
public import Mathlib.CategoryTheory.Limits.Elements
/-!
# Finite-limit-preservi... |
2,216 | lean_file_chunk | fe0a700f8183416691d660a8d0f90658a57df3a2179d1dcaca398e5a0e941f44 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.CategoryTheory.Limits.Preserves.Filtered
/-!
# Forgetful functor from `Over X` preserves cofiltered limits
Note that `Over.forget X : Over ... |
4,545 | lean_file_chunk | 1a44751a7487799092ef971b9213338f9ef348ceff6fb215fb50f0d33a84ba36 | 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.Limits.Preserves.Shapes.Kernels
public import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
/-!
# Action of bifunctors on co... |
17,497 | lean_file_chunk | e57e18b79ba45123c71dbb5f7589fc015e2a25dfc987ea315d6251a0fe938d7c | 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, Joël Riou
-/
module
public import Mathlib.CategoryTheory.Limits.Fubini
public import Mathlib.CategoryTheory.Functor.Currying
public import Mathlib.CategoryTheory.Limits.... |
23,989 | lean_file_chunk | 4fe504e64680b77970fae28af8bc7191d33d48cb1a537c6e55f7dda2c3f397a1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Reid Barton, Bhavik Mehta, Jakob von Raumer
-/
module
public import Mathlib.CategoryTheory.Limits.HasLimits
/-!
# Preservation and reflection of (co)limits.
There are va... |
12,664 | lean_file_chunk | 1e7489e51ad0930bd4dcdb36545474ab34e48cd1be336598eada0c7335143ec9 | lean_source_file | pkg_mathlib_source_file_chunks | [ReflectsLimitsOfSize.{w', w} G] : PreservesLimitsOfSize.{w', w} F where
preservesLimitsOfShape := preservesLimitsOfShape_of_reflects_of_preserves F G
/-- Transfer reflection of limits along a natural isomorphism in the diagram. -/
lemma reflectsLimit_of_iso_diagram {K₁ K₂ : J ⥤ C} (F : C ⥤ D) (h : K₁ ≅ K₂) [Reflect... |
3,157 | lean_file_chunk | 6845b7557b44b7bd2d1ad93e431371cc0feb736e7c1227fb4caf658660fbe89d | 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, Junyan Xu, Sophie Morel
-/
module
public import Mathlib.CategoryTheory.Limits.Creates
public import Mathlib.CategoryTheory.Limits.Types.Limits
public import Mathli... |
4,306 | lean_file_chunk | 1c64553bcf5ab8662cace9e897d8f9bc9434c1aa382eb482791531f98be032c7 | 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.Limits.Preserves.Basic
public import Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms
public import Mathlib.CategoryTheory.Limits... |
23,951 | lean_file_chunk | 55317fe36bfd9142daa535656edbde7b71ff459ae2c2eb78bd0caad0f707b363 | 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.Limits.Opposites
public import Mathlib.CategoryTheory.Limits.Preserves.Finite
/-!
# Limit preservation properties of `Func... |
23,971 | lean_file_chunk | 0351bdc8e07b6841be2ad3e080001f073ba5beed1f60415373e8f3e8dff78d1f | lean_source_file | pkg_mathlib_source_file_chunks | /-- If `F.rightOp : C ⥤ Dᵒᵖ` preserves finite limits, then `F : Cᵒᵖ ⥤ D` preserves finite
colimits. -/
lemma preservesFiniteColimits_of_rightOp (F : Cᵒᵖ ⥤ D) [PreservesFiniteLimits F.rightOp] :
PreservesFiniteColimits F where
preservesFiniteColimits J _ _ := preservesColimitsOfShape_of_rightOp J F
/-- If `F.unop... |
5,757 | lean_file_chunk | 962599cf993b3baebdfa9c19d9bace00a526a8b63ba850b1da09b18134905424 | lean_source_file | pkg_mathlib_source_file_chunks | /-- If `F : Cᵒᵖ ⥤ D` reflects finite limits, then `F.rightOp : C ⥤ Dᵒᵖ` reflects finite
colimits. -/
lemma reflectsFiniteColimits_rightOp (F : Cᵒᵖ ⥤ D) [ReflectsFiniteLimits F] :
ReflectsFiniteColimits F.rightOp where
reflects J _ _ := reflectsColimitsOfShape_rightOp J F
/-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` reflects finite li... |
4,662 | lean_file_chunk | 11b7dedadb7c550e94ef52a79d05b7132a1565f9a77754eac7b5e9a530f660a6 | 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.Limits.FunctorCategory.Basic
public import Mathlib.CategoryTheory.Limits.Shapes.Grothendieck
/-!
# Colimits on Groth... |
6,207 | lean_file_chunk | a3be1e9d81d3a9bd07eb13ea8984c4ad1be3a9985a81b12b1a6c608d3a5888dd | 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, Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Limits.Preserves.Basic
/-!
# Isomorphisms about functors which preserve (co)limits
If `G` preserves limits, a... |
13,246 | lean_file_chunk | 0a99aae68c81855ccc6832c048b8208ff288b11936668df62f3701864b4cff0b | 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.FunctorCategory.Basic
public import Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts
public import Mathli... |
2,454 | lean_file_chunk | cc3ab4f2d9b22760d22e1395e624ac9802bf7aa9d2f55b00ba3dc8f389169202 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.CategoryTheory.Limits.FunctorCategory.Basic
public import Mathlib.CategoryTheory.Limits.Shapes.Products
/-!
# (Co)products in functor cat... |
1,310 | lean_file_chunk | 4ee39143c3444a999d7cbe6de9de8bdace54d0ba064730b7872407b0a67711cc | 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.Limits.FunctorCategory.Basic
public import Mathlib.CategoryTheory.Limits.Shapes.Terminal
/-!
# Initial and terminal objects in the... |
1,319 | lean_file_chunk | f8255a47eef0fa1093ad44f851384936763a4fc4f14be34d8dc367bc83a038fd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yaël Dillies, Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Joël Riou
-/
module
public import Mathlib.CategoryTheory.Limits.FunctorCategory.Basic
public import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels
/-!
... |
1,626 | lean_file_chunk | 121fd63f66b42ebafa3f600f63ab99d921171e30053050b93e1a78335231df90 | 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.Limits.Shapes.Images
public import Mathlib.CategoryTheory.Subfunctor.Image
public import Mathlib.Tactic.CategoryTheor... |
4,948 | lean_file_chunk | f3214269582278296ae66711f858e212d8c3d7213005c9c68a953475f1a63761 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.CategoryTheory.Limits.FunctorCategory.Basic
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
/-!
# Pullbacks in fu... |
15,119 | lean_file_chunk | 07b7d6fb6bb6aa7e18b5b6b3c198a3df08be720b179fe8e313756679664ffe44 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Reid Barton, Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPul... |
2,408 | lean_file_chunk | 4df0a148bf0c9dc2644d2129ef98322c0662caaf9881289ff546be6dc4891349 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Reid Barton, Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Limits.Connected
public import Mathlib.CategoryTheory.Limits.Constructions.Over.Products
publi... |
8,484 | lean_file_chunk | cdcae5d1b083d1385193c2ae0fe36e7db52c5ccb9d729e9a23f190c78af5b7c7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Reid Barton, Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Limits.Preserves.Creates.Opposites
public import Mathlib.CategoryTheory.Comma.Over.Basic
publi... |
940 | lean_file_chunk | 7736d5d18c4d17d316dfaaf322c8c981b6e0ead905bf6b85eaf05f5cfc84e31f | 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.Limits.Shapes.IsTerminal
public import Mathlib.Order.Fin.Basic
/-!
# Limits and colimits indexed by `Fin`
In this file, we show t... |
1,040 | lean_file_chunk | 038a9c91b17debfac4dc8c0282ebd3cd5f3914ece9b93ea83792135810cdcca4 | 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.Order.InitialSeg
public import Mathlib.CategoryTheory.Category.Preorder
public import Mathlib.CategoryTheory.Limits.Cones
/-!
# Cocones associate... |
947 | lean_file_chunk | fe7727e6f6dfb4b1f792fc96715ba4249bdf04753682cc7a715a46a6d7eb9850 | 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.Preorder
/-!
# Limits and colimits indexed by preorders
In this file, we obtain the following very basic results
about lim... |
5,679 | lean_file_chunk | 53d863ae7122b93865888085b2f1e549cebfb1f65239a5cc5d51134d5529f8c4 | 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.ComposableArrows.Basic
public import Mathlib.CategoryTheory.Limits.Shapes.Preorder.WellOrderContinuous
public import Mathlib.Catego... |
3,879 | lean_file_chunk | eb59da91098590006a558b7b4844ff5b36c97fc469abbec43dc8bd93766a31b9 | 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.Comma
public import Mathlib.CategoryTheory.Limits.FunctorCategory.Basic
public import Mathlib.CategoryTheory.Limits.Shapes.P... |
4,386 | lean_file_chunk | 1b061412b4276b53336b832cece05f2f706e4db1a304e3f169391a91eabfb2d1 | 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.IsLimit
public import Mathlib.CategoryTheory.Limits.Shapes.Preorder.PrincipalSeg
public import Mathlib.CategoryTheory.Limits... |
12,139 | lean_file_chunk | 2948bad3ec47582c2dfb32e224b01f263d61fe271293aaa92a0a7b1b66e4bd2e | 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, Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.RegularMono
public import Mathlib.CategoryTheory.Limits.Shapes.Kernels
public import Mathlib.Cate... |
14,779 | lean_file_chunk | 148c4e1b08e331d129ac862bf5973e059115e0feda01dd8caa4c602c4c3eaeef | 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.NormalMono.Basic
public import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts
public import Mathlib.Cate... |
14,271 | lean_file_chunk | 4eac1b000e2ec60fc74a5b1084563f74c61b6e7fc81ef009a7b81293851c35b9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Floris van Doorn
-/
module
public import Mathlib.CategoryTheory.Limits.Opposites
public import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts
/-!
# Products and copr... |
1,579 | lean_file_chunk | c88dc41081f930310b53ced1add3692d069bb6a7900aecb8e7a6d9a90e5b913e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Floris van Doorn
-/
module
public import Mathlib.CategoryTheory.Limits.Opposites
public import Mathlib.CategoryTheory.Limits.Filtered
/-!
# Filtered colimits and cofilter... |
17,880 | lean_file_chunk | 4d39738508058d115b35299785bc1ce83102934c824e9d1e9c8f8bafa4a4cd6c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Floris van Doorn
-/
module
public import Mathlib.CategoryTheory.Limits.Opposites
public import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
public import Mathlib.Catego... |
3,596 | lean_file_chunk | 5af42120e11af2a63335360a5b8eb15f24cd336a22f662b75bbf1002630c621c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Floris van Doorn
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Kernels
/-!
# Kernels and cokernels in `C` and `Cᵒᵖ`
We construct kernels and cokernels in ... |
19,877 | lean_file_chunk | 78bad530629b15a613cac6d28c92f93a91573e2041de216b746d8fce0d14ec50 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Floris van Doorn
-/
module
public import Mathlib.CategoryTheory.Limits.Opposites
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
/-!
# Pullbacks a... |
23,946 | lean_file_chunk | fa330221de69a351c38815f11e5f067dfc93fc973cbbe3357f94f006c385d85e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Markus Himmel, Bhavik Mehta, Andrew Yang, Emily Riehl, Calle Sönne
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone
/-!
# HasPullback
`H... |
7,535 | lean_file_chunk | 0930e48540ed9a311ec9ae33e45ce98ff87b7670229f29b84b8da16ef65cbefd | lean_source_file | pkg_mathlib_source_file_chunks | def pushoutSymmetry [HasPushout f g] : pushout f g ≅ pushout g f :=
IsColimit.coconePointUniqueUpToIso
(PushoutCocone.flipIsColimit (pushoutIsPushout f g)) (colimit.isColimit _)
@[reassoc (attr := simp)]
theorem inl_comp_pushoutSymmetry_hom [HasPushout f g] :
pushout.inl _ _ ≫ (pushoutSymmetry f g).hom = pus... |
3,919 | lean_file_chunk | 0b29c6d721b52f43d7e07eb75ae4e0edf1a5a10fb6d2f83d4c58b9c48a12c417 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 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.Limits.Shapes.Products
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equifibered
public import Mathlib.CategoryTh... |
19,500 | lean_file_chunk | 24c24372f0aa2fe7f735a18b802ebce1d76f0eff1a40e008c802b2bb9b409dda | 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, Jack McKoen
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs
public import Mathlib.CategoryTheory.Adjunction.Parametrized
/-!
# Leibniz Con... |
5,802 | lean_file_chunk | f0e55d8464f0f472f60a721d6222bd3691c71ed9c418752e5c72bf65cb760124 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
public import Mathlib.CategoryTheory.MorphismProperty.Composition
/-!
# Equifibered n... |
13,773 | lean_file_chunk | 140532c67c0887a1c527d5b1a4d177b788551ed308dc04af5723b5d91e3e33ca | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting
/-!
# Associativity of pullbacks
This file shows that pullbacks (and pushouts) are associativ... |
22,677 | lean_file_chunk | c64ec277fc96049e0d05008e586d8082986566500b1848754f89486e37a36725 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Markus Himmel, Bhavik Mehta, Andrew Yang, Emily Riehl, Calle Sönne
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan
/-!
# PullbackCone
This f... |
4,481 | lean_file_chunk | 9c5583220f46c30b1e6dd26064865196c473512cdd4d71ed4110e63197f1bba9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.MorphismProperty.Limits
public import Mathlib.CategoryTheory.Square
/-!
# Commutative squares that are pushout or pullback squares... |
23,507 | lean_file_chunk | f447243e4bea0c3597f296b2c1de88dd487ba4de3f289fe3fe263dce8d3e25ab | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Calle Sönne
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
/-!
# Pasting lemma
This file proves the pasting lemma for pullbacks. That i... |
16,727 | lean_file_chunk | 196a60fadffaf77b3df93af0de7a3821f3b081a312ac8acddea9f048ca4ea62c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Andrew Yang
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso
/-!
# Pullbacks and monomorphisms
This file provides some results about interaction... |
15,191 | lean_file_chunk | d60070c787e215b16771b94f9c4deffafb943b6583b01ef1964c25976c190db5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Markus Himmel, Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks
public import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
/... |
3,085 | lean_file_chunk | a8b93d19dc2b8ed8633bfd22612ce06010252e4b19356455c494502d654d98db | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.CategoryTheory.IsConnected
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs
/-!
# Pullbacks commute with connecte... |
7,494 | lean_file_chunk | e633cfe58e52bc670cd48db82e00b2fc62258457f4bb20840dada470026ad4b1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
/-!
# The pullback of an isomorphism
This file provides some basic results about the pull... |
4,932 | lean_file_chunk | 9e622dd308d41a29ae94babb843e061ca165422c71a816fd47bfd3e4563961b8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs
/-!
# Equalizers as pullbacks of products
Also see `CategoryTheory.Limits.Construction... |
8,689 | lean_file_chunk | 019e3da253f670df7ada4168b9b6541411be291e4db24028327eb0f7c11bf2b8 | 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.Shapes.Pullback.IsPullback.Basic
/-!
# Chosen pullbacks
Given two morphisms `f₁ : X₁ ⟶ S` and `f₂ : X₂ ⟶... |
755 | lean_file_chunk | e2f8c40d1d183ce732e072f56c17126404b405a451125749c972a799e031770c | 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, Joël Riou, Calle Sönne
-/
module -- shake: keep-all
public import Mathlib.CategoryTheory.Category.Init
public import Mathlib.Data.Finset.Attr
public import Mathlib.Tactic.... |
23,938 | lean_file_chunk | 5d177aa66fab71baa62ec6be1884656f35df6f8f96bcb7db42493059a0c6affd | 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.CatCommSq
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform
/-! # Categorical pul... |
6,249 | lean_file_chunk | a5c63f113348e456279963bfd36f0419ac2802962352cbce8b2cd901bec75c62 | lean_source_file | pkg_mathlib_source_file_chunks | (app component of the) map component of a pseudofunctor from the bicategory of
categorical cospans with value in pseudofunctors
(its value on the categorical cospan `F, G` being the pseudofunctor
`precompose F G|>.obj _`). -/
@[simps!]
instance precomposeObjTransformObjSquare
{X : Type u₇} {Y : Type u₈} [Category.{... |
14,597 | lean_file_chunk | 97b68b9dca717b3b5020428b19dd9da346f73e0677bcdf093aedae75e239a4c4 | 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.CatCommSq
/-! # Morphisms of categorical cospans.
Given `F : A ⥤ B`, `G : C ⥤ B`, `F' : A' ⥤ B'` and `G' : C' ⥤ B'`,
this... |
10,935 | lean_file_chunk | bfa76c914af376dac372a16f1035e1c0adad4a8177bb52932b57769a45ad33cb | 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, Joël Riou, Calle Sönne
-/
module
public import Mathlib.CategoryTheory.Limits.Constructions.ZeroObjects
public import Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
... |
23,960 | lean_file_chunk | ba1f048ed51d1a7d994599131a64ebe42f95d3044df8a4e91026a5ab361277b7 | 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, Joël Riou, Calle Sönne
-/
module
public import Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPul... |
9,229 | lean_file_chunk | 998ad95650fdb3616c31373efe035509ba04cdc97ee502ae0ce01c4062e763eb | lean_source_file | pkg_mathlib_source_file_chunks | simp only [← cancel_epi f, s.condition, sq.w_assoc, IsIso.hom_inv_id_assoc])
theorem of_horiz_isIso [IsIso f] [IsIso inr] (sq : CommSq f g inl inr) : IsPushout f g inl inr :=
of_horiz_isIso_epi sq
theorem of_vert_isIso_epi [Epi g] [IsIso inl] (sq : CommSq f g inl inr) : IsPushout f g inl inr :=
(of_horiz_isIso_ep... |
15,378 | lean_file_chunk | d3c0674e8aab70a3db2ff792a038eac6950bfe4a25f0a8b00d88141b671e8cbd | 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, Joël Riou, Calle Sönne
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks
/-!
# Pullback and pushout squares
We provide another API for pu... |
1,567 | lean_file_chunk | cca05c66adff86d5aa4cac62470d446b999c8eeb739e0c59759d44ad8a38f3b6 | 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.Limits.Shapes.Kernels
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs
/-!
# Horizontal maps in a pullb... |
9,412 | lean_file_chunk | 7e816e8232ccf95b27de06dd31f50fbf1d5a3b606b543100afdd77e448dbebf3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.CategoryTheory.Limits.Creates
public import Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits
public import Mathlib.CategoryTheory.Limits.... |
23,997 | lean_file_chunk | 7dd4549898e2b93af0fb73dfa4d3a9ebc1eee9dc867ae33f5aa17fe53f8088cb | 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.Limits.Preserves.Opposites
public import Mathlib.CategoryTheory.Limits.Preserves.Creates.Finite
/-!
# Limit creation... |
5,865 | lean_file_chunk | 37a3e9e39b1e1f3d7089f6d794cd406651f47fbbfb520367ecd7a629c3b97c8c | lean_source_file | pkg_mathlib_source_file_chunks | CreatesFiniteColimits F.rightOp where
createsFiniteColimits J _ _ := createsColimitsOfShapeRightOp J F
/-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` creates finite limits, then `F.unop : C ⥤ D` creates finite
colimits. -/
@[implicit_reducible]
def createsFiniteColimitsUnop (F : Cᵒᵖ ⥤ Dᵒᵖ) [CreatesFiniteLimits F] :
CreatesFiniteColimit... |
1,117 | lean_file_chunk | 75817a3d1b13df32e4043b967476b905aec008ea7b9b091c8a24cb2c8ca631bb | 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.Creates
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
/-!
# Creation of limits and ... |
15,833 | lean_file_chunk | cd69a824717796834266fe30d17281ed05f6b8d9f39fd0ce0e3d2be13b56faf9 | 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.Limits.Shapes.BinaryBiproducts
public import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero
/-!
# Preservation of bip... |
7,941 | lean_file_chunk | eb2979d59904c4846136947b306b204289bf2c8601cd83f90f9fc78ef4fb6ce7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Products
public import Mathlib.CategoryTheory.Limits.Preserves.Basic
/-!
# Preserv... |
8,761 | lean_file_chunk | 3bf69f376eabe9ba7979f91a64158d6b559734d02515f19596e9aedf6b41914f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Terminal
public import Mathlib.CategoryTheory.Limits.Preserves.Basic
/-!
# Preserving terminal object
Constru... |
3,116 | lean_file_chunk | a78c744dd04d18519141e8b4e2d80aff1d643f5485339b7fb82a6e49324541f6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yaël Dillies, Moisés Herradón Cueto. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Moisés Herradón Cueto
-/
module
public import Mathlib.CategoryTheory.Limits.Preserves.Finite
public import Mathlib.CategoryTheory.WithTerminal.FinCa... |
9,903 | lean_file_chunk | 2f3578241216d6f3a032483d678b1cd4359267809c57f02c0073f4c644b1c8be | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.SplitCoequalizer
public import Mathlib.CategoryTheory.Limits.Shapes.SplitEqualizer
public import Mathlib.Catego... |
13,616 | lean_file_chunk | 4d9c2b3f4820311f9c095aa48dffbe816fefc8299147e37a8337694085c92484 | 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.Limits.Shapes.Kernels
public import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero
/-!
# Preserving (co)kernels
Constr... |
4,231 | lean_file_chunk | 8b6402549bc4b4fc8bf827c5da0faf318947a6297c8168c1eaca770150992e40 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square
public import Mathlib.CategoryTheory.Limits.Yoneda
public import Mathlib.CategoryTheory.Limits.Preser... |
2,842 | lean_file_chunk | 243cb9839c5bae5375f8d0d962d6c9d1b613e429ee8da515adc694e5c8e02de5 | 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.Limits.Shapes.Multiequalizer
/-!
# Preservation of multicoequalizers
Let `J : MultispanShape` and `d : MultispanIndex J C`.
If `F... |
3,134 | lean_file_chunk | 98ee73a0f65612f082bf44e47c01de458e240379c742a2507a3c36609fa29ada | 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.Limits.Shapes.Preorder.WellOrderContinuous
public import Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfShape
public i... |
2,054 | lean_file_chunk | 0acf8b81d691af30f56c5aa1afe7a88c4e6c12e73624aa9d4cf9c7d5f7a04481 | 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
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Images
public import Mathlib.CategoryTheory.Limits.Constructions.EpiMono
/-!
# Preserving images
In this file... |
4,471 | lean_file_chunk | 2833b9e90d7eb3950984d78bcc7d858486e8ada53a03ed028c131f45890cf2b1 | 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.Images
public import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels
/-!
# Preservation of coimage-image co... |
8,033 | lean_file_chunk | 71e0dbb6523d3fd438de8bf894d29473de8e4d0f00c3d8abfe3f49493cd323a2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
public import Mathlib.CategoryTheory.Limits.Preserves.Basic
/-!
# Preserving binary products
C... |
8,280 | lean_file_chunk | b55ce035eb0c7c7ddca085cf308b7051ed19bf11c57bf72688a6cf39058118f5 | 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.Limits.Preserves.Shapes.Terminal
public import Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms
/-!
# Preservation of ze... |
14,070 | lean_file_chunk | a0ad7cf4c8bf825fbc4c0c46761895441580b11316ab34dad75be041205e3b0b | 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, Andrew Yang
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
public import Mathlib.CategoryTheory.Limits.Preserves.Basic
public import Mat... |
4,410 | lean_file_chunk | 222684898a385819655b150695882217f6acda31e0a51fbe405f0f58b5bbb2b0 | 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.Functor.KanExtension.Adjunction
public import Mathlib.CategoryTheory.Limits.Final
/-!
# Finality on Costructured Arr... |
23,982 | lean_file_chunk | c11be2df81513138289f0e39947af16f3780c9ce5375b084cb74d3fb7ce42d17 | 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: Adam Topaz, Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Comma.Basic
public import Mathlib.CategoryTheory.PUnit
public import Mathlib.CategoryTheory.Limits.Shapes.IsTermi... |
18,232 | lean_file_chunk | b82d941dc436f1c4600048a7af9ad577727e13d16ae4b117d63d2ab20f0db320 | lean_source_file | pkg_mathlib_source_file_chunks | instance (F : B ⥤ C) (G : C ⥤ D) (S : D) [F.Full] : (pre F G S).Full :=
show (Comma.preLeft _ _ _).Full from inferInstance
instance (F : B ⥤ C) (G : C ⥤ D) (S : D) [F.EssSurj] : (pre F G S).EssSurj :=
show (Comma.preLeft _ _ _).EssSurj from inferInstance
/-- If `F` is an equivalence, then so is the functor `(F ⋙ ... |
5,339 | lean_file_chunk | a79601ea8d1640cc698e38e59a78503cb94116ca71151b5983cc5006f904ffd0 | 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.Comma.StructuredArrow.Basic
public import Mathlib.CategoryTheory.Grothendieck
/-!
# Structured Arrow Categories as s... |
3,130 | lean_file_chunk | dff7e96d65bba8098807093a811bbbe0066329825d28b882380c94e86bc46ae0 | 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.Comma.StructuredArrow.Basic
public import Mathlib.CategoryTheory.EssentiallySmall
public import Mathlib.CategoryTheory.Obje... |
3,780 | lean_file_chunk | 0bbf24513464c4843f429c47967948fb7ded16d5060287d7934d55a7b6ccf815 | 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.Comma.StructuredArrow.Basic
/-!
# Structured arrow categories on `Comma.map`
We characterize structured arrow categ... |
3,015 | lean_file_chunk | 5a37828bd6fdcf96f0a17060592456648a524ebb5beccc101fe8d1b2a693639d | 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.MorphismProperty.Comma
public import Mathlib.CategoryTheory.Limits.Shapes.StrictInitial
/-!
# `Over X` when `C` has ... |
23,999 | lean_file_chunk | 0ceb9c4aef8996924c519ddb07de7537933d78b024d3ae40ef757a0d068ed301 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
public import Mathlib.CategoryTheory.Category.Cat
/-!
# Over and under categor... |
23,953 | lean_file_chunk | 9d46013ef4ec85fa247a308c674827045904be4644cd2e0326200be600bf238f | lean_source_file | pkg_mathlib_source_file_chunks | -/
@[simps! hom_right inv_right]
def isoMk {f g : Under X} (hr : f.right ≅ g.right)
(hw : f.hom ≫ hr.hom = g.hom := by cat_disch) : f ≅ g :=
StructuredArrow.isoMk hr hw
@[simp]
lemma eqToHom_right {f g : Under X} (h : f = g) :
(eqToHom h).right = eqToHom (by rw [h]) := by
subst h
rfl
@[reassoc (attr := ... |
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