chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
3,490 | lean_file_chunk | 969284b3743a80fca7e4f6c6a0903bcd822606b3affce215697aa8481821cd28 | 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.MorphismProperty.Composition
public import Mathlib.CategoryTheory.ObjectProperty.Opposite
/-!
# Object properties tr... |
3,078 | lean_file_chunk | 82b1820e96364813b43b99e3c013ad1b8921ae033b6f25881c6e224e664b8af0 | 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.ObjectProperty.CompleteLattice
public import Mathlib.CategoryTheory.Sites.Hypercover.Zero
/-!
# Locality conditions ... |
15,079 | lean_file_chunk | 167a106ee873ab7e5cc7367e380fa1a83e36869ceb7efc5e7ee4603e200c7cb0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.ObjectProperty.Small
public import Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape
public import Mathlib.CategoryTheory.ObjectP... |
23,966 | lean_file_chunk | 07131dc26c0c5596fcfa83cbaa5f04a401628b64101ef63c791788488f79ff1b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
public import Mathlib.Algebra.Group.Ext
public import Mathlib.CategoryTheory.Limits.Preserves.Sh... |
21,860 | lean_file_chunk | ca62f226454ccabcc8a5d7fd954d507f99a0d7f038f344870d08a6df70b4e846 | lean_source_file | pkg_mathlib_source_file_chunks | obtain ⟨q : Y ⟶ T, hq : b.snd ≫ q = m - (b.fst ≫ f + b.snd ≫ g)⟩ :=
CokernelCofork.IsColimit.desc' hb _ h₁'
rw [← sub_eq_zero, ← hq, ← Category.id_comp q, ← b.inr_snd, Category.assoc, hq, h₂',
comp_zero]
set_option backward.isDefEq.respectTransparency false in
/-- Every split epi `f` with a kerne... |
12,923 | lean_file_chunk | 0da16206935bd3e31fc72d9471a2a3b230623239f2b05a0c68af84c1597d91b0 | 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, Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Limits.ExactFunctor
public import Mathlib.CategoryTheory.Limits.Preserves.Finite
public import Mathlib.CategoryTheo... |
4,421 | lean_file_chunk | 1512910cf2a84bf2f0b44bf7f4e2d444dee163feb6167a5ffc395d17d46bfd55 | 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.GroupTheory.EckmannHilton
public import Mathlib.Tactic.CategoryTheory.... |
3,349 | lean_file_chunk | 00e3f2ccc44f4b0153405b028b298296cf4079059e61af472d536246885b14c6 | 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, Johan Commelin, Joël Riou
-/
module
public import Mathlib.Algebra.Group.TransferInstance
public import Mathlib.Algebra.Module.Equiv.Defs
public import Mathlib.... |
9,497 | lean_file_chunk | 4f94c2b221c3dca4ecfc8711f49f97d12605e72ec23c7728cc9d88122c675a6e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Jakob von Raumer
-/
module
public import Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers
public import Mathlib.CategoryTheory.Limits.Preserv... |
1,047 | lean_file_chunk | c580da38852bfa32820ee875d8cd08b42d5ae2455be7f89c395ea8da9fbff0fb | 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.Indization.Category
public import Mathlib.CategoryTheory.Preadditive.Transfer
public import Mathlib.CategoryTheory.P... |
3,216 | lean_file_chunk | 62f801a26a8ef60c5ad10210033b33b89929e7a7e309acc6c32d7a6da0175a5e | 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.CommGrp_
public import Mathlib.CategoryTheory.Preadditive.Biproducts
/-!
# Commutative group objects in additive ... |
17,262 | lean_file_chunk | 82c2ffb17e861d256b0206234a4213f8e380e804bdcfef1c575c5cbccc788641 | 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, Jakob von Raumer
-/
module
public import Mathlib.Algebra.Group.TransferInstance
public import Mathlib.Algebra.Group.Hom.Defs
public import Mathlib.Algebra.Group.Action.U... |
7,578 | lean_file_chunk | 79e8e182e915b2d5bdf7a89b323df5cba76269d8d2909f938c43ff4512ce2780 | 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: Markus Himmel, Kim Morrison
-/
module
public import Mathlib.Algebra.Group.Ext
public import Mathlib.CategoryTheory.Simple
public import Mathlib.CategoryTheory.Linear.Basic
public import... |
2,400 | lean_file_chunk | a5138de49036614e53766119780b73485e7aaf5a83e6f463ee0b4628c1232d29 | 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.Constructions.Filtered
public import Mathlib.CategoryTheory.Preadditive.Basic
public import Mathlib.Algebra.BigOpera... |
641 | lean_file_chunk | 6a84f47d275f9e59bc2c945bb9b8ecbe502593caa27b70fcd23acf651f2ef9be | 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.Basic
public import Mathlib.CategoryTheory.SingleObj
/-!
# `SingleObj α` is preadditive when `α` is a ring.
-/
... |
4,552 | lean_file_chunk | f4feb7007f25009ba1c647cfdc2454e95f5280e789fa236d8d1c66c6c8ed2d52 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
module
public import Mathlib.CategoryTheory.Preadditive.Basic
public import Mathlib.CategoryTheory.Endofunctor.Algebra
public import Mathlib.CategoryTheory.P... |
2,029 | lean_file_chunk | 89005f3e5f75c76301328233c2772271e804c3610775149f871fa149ca2f3eb5 | 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.Algebra.Group.TransferInstance
public import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
/-!
# Pulling back a preadditive st... |
7,573 | lean_file_chunk | 4ba5037acfc612fcbb62e7c3bfee81e144e37c3944c2a81339813a7dca963308 | 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.Basic
public import Mathlib.CategoryTheory.Preadditive.Biproducts
public import Mathlib.LinearAlgebra.Matrix.Invariant... |
3,168 | lean_file_chunk | e8ce07d8dbbeb259ec17a6108a951f537ca9e25aead46a6ac687ae3f90da5609 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.CategoryTheory.Preadditive.Basic
public import Mathlib.Algebra.BigOperators.Group.Finset.Basic
/-!
# Preadditive structure on functor c... |
20,676 | lean_file_chunk | 72ddefbbf6cb3e881d8374b7109cdb080bae66a4622c699c6bf584e9a2b25555 | 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.Algebra.BigOperators.Group.Finset.Pi
public import Mathlib.Algebra.BigOperators.Pi
public import Mathlib.Algebra.Opposites
public import Mat... |
4,543 | lean_file_chunk | 5094c52f6fe1a174d2cb7834b936474d7f540e01611c607798f5f8254eb32008 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
module
public import Mathlib.CategoryTheory.Preadditive.Basic
public import Mathlib.CategoryTheory.Monad.Algebra
public import Mathlib.CategoryTheory.Preaddi... |
8,771 | lean_file_chunk | 4975b393d66a17deea4739dc48c4e7bd9621bb9f4c26921d290b8d373327b756 | 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.Presentable.LocallyPresentable
public import Mathlib.CategoryTheory.ObjectProperty.ColimitsCardinalClosure
public import Mathlib.Ca... |
5,191 | lean_file_chunk | 253c92ff69d0e9c03c1a0a892eba55b72f2076ad21e1598dbac030f1d9614408 | 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.Filtered
public import Mathlib.CategoryTheory.Limits.Preserves.Filtered
public import Mathlib.CategoryTheory.Limits.Type... |
3,816 | lean_file_chunk | 1a9902b691a496f5f96e560a44794eb501e8d5c71fb8a50635c39f366c15adea | 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.Presentable.CardinalFilteredPresentation
/-!
# Locally presentable and accessible categories
In this file, we define the notion o... |
1,486 | lean_file_chunk | c0f7db21a44fd8db62ea9af9ffb57adf5af24135522bbca8a6292dcf69035560 | 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.Presentable.Basic
public import Mathlib.CategoryTheory.ObjectProperty.Retract
/-!
# Presentable objects are stable under retracts
... |
3,556 | lean_file_chunk | d97296051b05cf8578ad7543bada44425a1115f552ff8db296fd3031a5887908 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Filtered.Final
public import Mathlib.CategoryTheory.Functor.KanExtension.Dense
public import Mathlib.CategoryTheory.Presentable.Loc... |
2,392 | lean_file_chunk | d50985c82fafc96eaece6d9b821fcc83f42fb7074479767a1a236f8add1a3aed | 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.Presentable.CardinalFilteredPresentation
/-!
# Accessible categories are essentially large
If a category `C` satisfies `HasCardin... |
3,767 | lean_file_chunk | bf68f984f40b81e88577eafe45993b14fd578fe4d81cd4ece4a9655aa2a68ad8 | 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.Generator.Presheaf
public import Mathlib.CategoryTheory.Limits.FunctorCategory.EpiMono
public import Mathlib.CategoryTheory.Present... |
5,312 | lean_file_chunk | bfef450a9e3a2251f006dcf01773a3117b882936d1fbb67990eebbbc272a956c | 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.Presentable.Basic
public import Mathlib.CategoryTheory.Limits.Types.Filtered
public import Mathlib.CategoryTheory.Types.Set
/-!
# ... |
6,633 | lean_file_chunk | bc5b10feac52d9a757fb63ba7fe1c9eaec56e42614d0ee2f5772a3284d72dec1 | 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.Presentation
public import Mathlib.CategoryTheory.Presentable.Finite
/-!
# Presentation of a colimit of objec... |
13,156 | lean_file_chunk | 95ab82a6f52f3161d9018ead84dd9c3051bedd007adecbca13b8cbdf82068092 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Adjunction.Limits
public import Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant
public import Mathlib.CategoryTheory... |
7,536 | lean_file_chunk | 242ee6e066cf0bda98b219ab58b3521c45cae842e955759d4264945ab444eb6b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.ObjectProperty.Small
public import Mathlib.CategoryTheory.Presentable.Limits
public import Mathlib.CategoryTheory.Presentable.Retra... |
4,426 | lean_file_chunk | 3bf13520898e6efe331597fd2d09a4fb2a45dbda0c0098efcab1a7b313933f74 | 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.Presentable.LocallyPresentable
public import Mathlib.CategoryTheory.Monad.Limits
/-!
# Presentable objects and adjunctions
If `ad... |
20,750 | lean_file_chunk | 11348245a7cbeb1b8bdd5660263feb0bf813c6d61e69c3af92162170f4a8c0ac | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Filtered.Final
public import Mathlib.CategoryTheory.Limits.Final
public import Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
... |
14,622 | lean_file_chunk | 632ce0ac80b5c4309e7b58625ccc71b959f6fb2699f2994f48d4dba561f28bb0 | 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.Filtered.Final
public import Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers
public import Mathlib.CategoryTheory.Comma.Cardina... |
19,728 | lean_file_chunk | 1a175ee50d6834aaa4faf1f1cb944ec6f3a7329d7fbbc3039fbe13388083d3e2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Adjunction.PartialAdjoint
public import Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
public import Mathlib.CategoryTheory.Lo... |
8,886 | lean_file_chunk | e932ca3e82f51803eb1e1fc5d1128399956e8df762e5ee525b18866bcb3d8128 | 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.Types.Filtered
public import Mathlib.CategoryTheory.Limits.Yoneda
public import Mathlib.CategoryTheory.Presentable.Basic
pub... |
849 | lean_file_chunk | ee52559aefcb15b07b67f707f02cd23aae87977a5ff04b2bdcf331081aedd3ba | 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.MorphismProperty.Limits
public import Mathlib.CategoryTheory.Limits.Types.Pullbacks
/-!
# Stability properties of epimorphisms in ... |
16,865 | lean_file_chunk | 1bc9d7e442dd7dd1e5369c0fab249b218285a0ff33dd1b89888784aac87af45a | 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: Stephen Morgan, Kim Morrison, Johannes Hölzl, Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Elementwise
public import Mathlib.CategoryTheory.EpiMono
public import Math... |
802 | lean_file_chunk | 771d8b2743cb7604113235076c532802e0766471ce5832496e3dcdbcb3f44938 | 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.Category.Preorder
public import Mathlib.CategoryTheory.Types.Basic
public import Mathlib.Data.Set.Basic
/-!
# The functor from `Se... |
3,416 | lean_file_chunk | 792cacff9790c2fa127fed88edbb45d3e0e6d726ee10850767d9c00aa0639e4f | 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.Connected
public import Mathlib.CategoryTheory.Limits.Types.Filtered
public import Mathlib.CategoryTheory.Limits.Types.Pusho... |
1,567 | lean_file_chunk | e832110c9f95633aacb759948996fb3eac5d04f95ffc5775067830cf284dcff0 | 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: Stephen Morgan, Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Products.Basic
/-!
# Lemmas about functors out of product categories.
-/
public section
open CategoryTheo... |
13,430 | lean_file_chunk | 0c34d54494944c8a0a0a8181a43ddbda14e033d9c5cf9b955f592c0ed61f33ca | 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: Stephen Morgan, Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Functor.Const
public import Mathlib.CategoryTheory.Opposites
public import Mathlib.Data.Prod.Basic
/-!
# Car... |
2,502 | lean_file_chunk | 7e62a5a2dd24e6aba6d77044ab8c44b91b2ca1ba2e98226a05caa18f1c3b8d90 | 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: Stephen Morgan, Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Products.Basic
/-!
The associator functor `((C × D) × E) ⥤ (C × (D × E))` and its inverse form an equivalenc... |
1,919 | lean_file_chunk | a1b670b28f423dbba68168b923353a5427549825f672e6fc02394b1d5b35f15c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Shanghe Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shanghe Chen
-/
module
public import Mathlib.CategoryTheory.Products.Basic
public import Mathlib.CategoryTheory.Discrete.Basic
/-!
# The left/right unitor equivalences `1 × C ≌ C` and ... |
2,251 | lean_file_chunk | a9866004cc47ef710bd7df376baa8e8109ae8d158a97bc9ad2f2e127ee4f8bc2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.ComposableArrows.Basic
/-!
# API for compositions of two arrows
Given morphisms `f : i ⟶ j`, `g : j ⟶ k`, and `fg : i ⟶ k` in a c... |
5,101 | lean_file_chunk | 796ada31ed06857a1be2a93eeb33cd13809f9933ef4df7c0ec15401fe3c27999 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.ComposableArrows.Basic
/-!
# API for compositions of four arrows
Given morphisms `f₁ : i₀ ⟶ i₁`, `f₂ : i₁ ⟶ i₂`, `f₃ : i₂ ⟶ i₃`, ... |
23,994 | lean_file_chunk | 6e591c6d1f0532e298c7070e41f9564fcda9f4c3d90c77875c20a1876abd0b0b | 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.Group.Nat.Defs
public import Mathlib.CategoryTheory.Category.Preorder
public import Mathlib.CategoryTheory.Comma.Arrow
public import Mathl... |
12,731 | lean_file_chunk | bfca64c64340c44209a7b48ab9736c1d9200eb657cce4858f9e60f461a607f3d | lean_source_file | pkg_mathlib_source_file_chunks | @[simp]
lemma homMk₃_app_three : (homMk₃ app₀ app₁ app₂ app₃ w₀ w₁ w₂).app ⟨3, by valid⟩ = app₃ :=
rfl
end
@[ext]
lemma hom_ext₃ {f g : ComposableArrows C 3} {φ φ' : f ⟶ g}
(h₀ : app' φ 0 = app' φ' 0) (h₁ : app' φ 1 = app' φ' 1) (h₂ : app' φ 2 = app' φ' 2)
(h₃ : app' φ 3 = app' φ' 3) :
φ = φ' :=
hom_e... |
3,423 | lean_file_chunk | 58b3338805d9d32b5afd3b8f26385575a75d70516c89d08487c401ef787ec945 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.ComposableArrows.Basic
/-!
# API for compositions of three arrows
Given morphisms `f₁ : i ⟶ j`, `f₂ : j ⟶ k`, `f₃ : k ⟶ l`, and t... |
1,255 | lean_file_chunk | 51ba4a1c7d85c6f30ee801b4bcf02b0c26bafde7d0b4641f66a4a0b8a0413a91 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.ComposableArrows.Basic
/-!
# Functors to `ComposableArrows C 1`
-/
@[expose] public section
universe v u
namespace CategoryThe... |
5,302 | lean_file_chunk | 0595bb167c3db86c7b77dfadb68fc86d496935ea49f5fca374d7388ac57558a2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour
-/
module
public import Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong
public import Mathlib.CategoryTheory.LocallyCartesianClosed.Over
public imp... |
12,142 | lean_file_chunk | f3c7b5f8c8ac3f5999cb71a81473756ea88eca178775439bbab1d25f311958ff | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour
-/
module
public import Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong
/-!
# Cartesian monoidal structure on slices induced by chosen pullbacks
... |
16,180 | lean_file_chunk | 1775e899c6b25c9fd8bdfde7da415241b7febbcaa03fa7ab0407f5ea1a3bbbda | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour
-/
module
public import Mathlib.CategoryTheory.Comma.Over.Pullback
public import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
public import Mathlib.CategoryTheory.... |
8,536 | lean_file_chunk | ad9e38237d7a4ee46f059de349acb476fda81ecf5945ac9305c45787ec30d9dc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour
-/
module
public import Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong
/-!
# Exponentiable morphisms
We define an exponentiable morphism `f : I ... |
2,062 | lean_file_chunk | 446a254c6e095dac0ef5e127bf580ccb80f97d12ea869a8ece9567ec6ce75c9f | 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.Join.Basic
public import Mathlib.CategoryTheory.Sums.Basic
/-!
# Embedding of `C ⊕ D` into `C ⋆ D`
This file constructs a... |
6,738 | lean_file_chunk | c1a4a75c9938d2cadc3c791b7ff03cc8cad3a2d657a809a1c9041bfc762e0cd6 | 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.Join.Basic
public import Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor
/-!
# Pseudofunctoriality of categorical ... |
2,106 | lean_file_chunk | 699878b8ee023ae1638de8af9245a259657b103c8033a11052fbc84095b1c8af | 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.Join.Basic
public import Mathlib.CategoryTheory.Limits.Final
public import Mathlib.CategoryTheory.Limits.IsConnected
/-!
#... |
22,280 | lean_file_chunk | 734192550eb40c538b04a9f3cf2c999183498a0c9957b007fed07c9ae9837461 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Functor.Category
public import Mathlib.CategoryTheory.Products.Basic
/-!
# Joins of categories
Given categories `C, D`, t... |
4,738 | lean_file_chunk | 758e99ee0227c90bda5474373737d8f88dd6a2e6987fd6a2b8bf5569581c3dd6 | 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.Join.Basic
public import Mathlib.CategoryTheory.Opposites
/-!
# Opposites of joins of categories
This file constructs the... |
1,680 | lean_file_chunk | 8e0ce17fabe4090f71fb33019bd053e21939b0172aee7b8ff260abdba10ff212 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jacob Reinhold. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jacob Reinhold
-/
module
public import Mathlib.CategoryTheory.CopyDiscardCategory.Basic
/-!
# Deterministic Morphisms in Copy-Discard Categories
Morphisms that preserve the copy ope... |
2,217 | lean_file_chunk | b6e73f3ec1807e05ab3fcd1b053dabfb953b23c5e6a5c211cdfe46fd137718c0 | 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_
/-!
# Copy-Discard Categories
Symmetric monoidal categories where every object has a commutative
comono... |
1,862 | lean_file_chunk | b65596db54f8df5e4ca8890728740401cf10e223b0af91b192c74aceb0ada32f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jacob Reinhold. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jacob Reinhold
-/
module
public import Mathlib.CategoryTheory.CopyDiscardCategory.Basic
public import Mathlib.CategoryTheory.CopyDiscardCategory.Deterministic
public import Mathlib.Ca... |
1,980 | lean_file_chunk | d7de3d067b6c8d30a288cfea6b47fc2cc4b9e0e9d02ce67299fc0b56173a31e7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Gaëtan Serré. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gaëtan Serré
-/
module
public import Mathlib.CategoryTheory.Monoidal.Widesubcategory
/-!
# Copy-discard structures on wide subcategories
Given a monoidal category `C`, a morphism prop... |
279 | lean_file_chunk | eded8e2bbb19bb61f31583c2ebc1f4fbb5e250e4081151de6d5cb90dd30a3315 | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
import Mathlib.CategoryTheory.Category.Init
import Mathlib.Data.Finset.Attr
import Mathlib.Tactic.Common
import Mathlib.Tactic.Finiteness.Attr
import Mathlib.Tactic.SetLike
import Mathlib.Util.CompileInductive
deprecated_module (since := "2026-01-14") |
1,540 | lean_file_chunk | cf7d7d489ea72bc03eb6688ee1801c457eb582d6abef06bd16ce04517f12ac79 | 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: Stephen Morgan, Kim Morrison, Johannes Hölzl, Reid Barton
-/
module
public import Mathlib.CategoryTheory.Category.Preorder
public import Mathlib.CategoryTheory.Adjunction.Basic
public i... |
15,799 | lean_file_chunk | 4849d0a859111f1ed17853ed72c8155f09ec5780eef9241a2e5fdb3a21e0c9b4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Mario Carneiro and Emily Riehl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Emily Riehl
-/
module
public import Mathlib.Combinatorics.Quiver.ReflQuiver
public import Mathlib.CategoryTheory.Category.Cat
public import Mathlib.Cat... |
4,104 | lean_file_chunk | 51aa3154c9eb3ccc0f22443dc97a77ca4b5d2305811b3f0dfdd3fe82b85880a2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 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.Arrow
public import Mathlib.CategoryTheory.Limits.Shapes.Terminal
/-!
# The Factorisation Category of a Catego... |
5,431 | lean_file_chunk | 3b224f90b6e1020fd94a2701a03ee4654a937e9603491050e1121d7467d28151 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Category.Preorder
public import Mathlib.CategoryTheory.Limits.IsLimit
public import Mathlib.CategoryTheory.FinCategory.Basic
... |
6,888 | lean_file_chunk | 946aeba1985e54222ed961b25b528d661c04e76d852e5fc8528db2c33c01bc0a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.CategoryTheory.Category.Pointed
/-!
# The category of bipointed types
This defines `Bipointed`, the category of bipointed types.
## TODO
... |
1,357 | lean_file_chunk | 844d1f48928ff32cbeb38a0370ef3ca222ab8d4bf84853425aeaca2775de93dd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg
-/
module
public import Mathlib.Init
public import Aesop
/-!
# Category Theory Rule Set
This module defines the `CategoryTheory` Aesop rule set which is used by the
`... |
5,514 | lean_file_chunk | 115092a971c24b0e515f6e7b91b4cb1d151c585395ef3365928ea069acd537b1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.CategoryTheory.Category.Bipointed
public import Mathlib.Data.TwoPointing
/-!
# The category of two-pointed types
This defines `TwoP`, the ... |
4,956 | lean_file_chunk | bf3c91b6993c7ec8c6124a57de0c68cbf6f7777df4b867cfd6a32cae2f53c073 | 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, Uni Marx
-/
module
public import Mathlib.CategoryTheory.EssentialImage
public import Mathlib.CategoryTheory.Iso
public import Mathlib.CategoryTheory.Opposites
public impor... |
1,882 | lean_file_chunk | 3545947977d3b511ca0677a0315aaabca9f63b9dff0db77d555892de48220fc1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
module
public import Mathlib.CategoryTheory.Category.Basic
/-!
# The Kleisli construction on the Type category
Define the Kleisli category for (control) monads.
`Categor... |
17,024 | lean_file_chunk | e1beaa2a5c8518662ec8319a9c389ba285366ea4f10215802fb805d7457e9482 | 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: Stephen Morgan, Kim Morrison, Johannes Hölzl, Reid Barton
-/
module
public import Mathlib.CategoryTheory.Category.Init
public import Mathlib.Combinatorics.Quiver.Basic
public import Mat... |
6,542 | lean_file_chunk | dd21cba6255234a56f57fc1937b64a39d0b47abab500d1ef3412eb66163783a8 | 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.Equivalence
public import Mathlib.CategoryTheory.EqToHom
public import Mathlib.Data.ULift
/-!
# Basic API for ULift
This file c... |
6,690 | lean_file_chunk | 359c659de95c097190c819b523b47598cfa76e35654b19eec96550c14f72bfc1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.CategoryTheory.Category.Pointed
public import Mathlib.Data.PFun
/-!
# The category of types with partial functions
This defines `PartialFu... |
3,526 | lean_file_chunk | 2b223460d9083cd8375226b780871a9c500d6463784a886e63c0bea6eb04dd42 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.CategoryTheory.ConcreteCategory.Forget
public import Mathlib.CategoryTheory.Adjunction.Basic
/-!
# The category of pointed types
This defi... |
15,512 | lean_file_chunk | 364d5031418d4d9f4fe7e17f0ca9738d0e2a17ed389fbf1f69271908763a48de | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.CategoryTheory.Bicategory.Strict.Basic
public import Mathlib.CategoryTheory.ConcreteCategory.Bundled
public import Mathlib.CategoryThe... |
9,692 | lean_file_chunk | 15acd207a7791463cf0d0af6b170a7df783734205f4e62ca112de335a10749d7 | 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, Emily Riehl, Joël Riou
-/
module
public import Mathlib.CategoryTheory.Adjunction.Basic
public import Mathlib.CategoryTheory.Category.Cat
public import Mathlib.CategoryTheo... |
8,081 | lean_file_chunk | 00ce25d433ec9f111ccb989936fc0673f182d7118906571cb5b6203d0f502db2 | 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: Stephen Morgan, Kim Morrison, Johannes Hölzl, Reid Barton
-/
module
public import Mathlib.CategoryTheory.Equivalence
public import Mathlib.CategoryTheory.EqToHom
public import Mathlib.O... |
10,904 | lean_file_chunk | e4d1ee779928465505e9a17db9669170f13384ac3d74a1b197b72965ca34f63e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Hua. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Hua
-/
module
public import Mathlib.CategoryTheory.Groupoid.FreeGroupoid
public import Mathlib.CategoryTheory.Groupoid.Grpd.Basic
public import Mathlib.CategoryTheory.Adjunction.Re... |
532 | lean_file_chunk | 19bf3bd240c6415ea4317ad87959e802556ad60aca530d68c07b16ce560c1392 | 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.Groupoid
public import Mathlib.CategoryTheory.Discrete.Basic
/-!
# Discrete categories are groupoids
-/
@[expose] p... |
2,591 | lean_file_chunk | a000b4218e129a42bd0c6120e668225613e9bd0213f6340a444a415b68a8a654 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémi Bottinelli
-/
module
public import Mathlib.Algebra.Group.Basic
public import Mathlib.Algebra.Group.Equiv.Defs
public import Mathlib.CategoryTheory.Groupoid
public import Mathlib... |
23,535 | lean_file_chunk | ef5f83c61a85c4ccf930610374df21eb388627704d28b8e81f6cbaa1d98019e0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémi Bottinelli, Junyan Xu
-/
module
public import Mathlib.Algebra.Group.Subgroup.Defs
public import Mathlib.CategoryTheory.Groupoid.VertexGroup
public import Mathlib.CategoryTheory.... |
1,109 | lean_file_chunk | a84872018718ee1535d74be23b60d95fc72ce44fdf01c294d633b5ec997dadf3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémi Bottinelli
-/
module
public import Mathlib.CategoryTheory.Groupoid
public import Mathlib.Combinatorics.Quiver.Basic
/-!
This file defines a few basic properties of groupoids.
-... |
7,633 | lean_file_chunk | 92b4e99053a50f15bed54f5901b76377d3ac17a7abd680bc15839800f0242b80 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémi Bottinelli
-/
module
public import Mathlib.CategoryTheory.Groupoid
public import Mathlib.CategoryTheory.PathCategory.Basic
/-!
# Free groupoid on a quiver
This file defines th... |
11,958 | lean_file_chunk | 9b56c693988da99505bc6c8ff845a870a30a9f1e0ad561e183a0a3faa33a1213 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour
-/
module
public import Mathlib.CategoryTheory.Monoidal.Closed.Basic
public import Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts
public import Mathlib... |
2,818 | lean_file_chunk | e8d436468529e3e44f77f5c8a59a61c74dde43c2dc20d79f997ec7aed80e9472 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour
-/
module
public import Mathlib.CategoryTheory.Distributive.Monoidal
public import Mathlib.CategoryTheory.Limits.MonoCoprod
public import Mathlib.CategoryTheory.Monoi... |
3,668 | lean_file_chunk | d08ca670c2ad4595909a616eb590832f02a6f88edfaca031e879355a715aa4dd | 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.GuitartExact.VerticalComposition
/-!
# The opposite of a Guitart exact square
A `2`-square is Guitart exact iff the opposite (tra... |
7,863 | lean_file_chunk | 5469d4fcc0b57506adc31b2fa9283f73d4001b8211c530cf112802fdea80068a | 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.GuitartExact.Basic
public import Mathlib.CategoryTheory.Functor.KanExtension.Adjunction
/-!
# Guitart exact squares and Kan extens... |
6,232 | lean_file_chunk | ced8e95b3a5117e764665492b45411e3daf0974eb80b141bd9ec55e62e73b32a | 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.CatCommSq
public import Mathlib.CategoryTheory.GuitartExact.Basic
/-!
# Vertical composition of Guitart exact squares
In this fil... |
2,317 | lean_file_chunk | ad04622977dd828efc48640fde08aa835011e91797e41ada24a7a30cd8e7f6a9 | 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.GuitartExact.Basic
public import Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts
/-!
# Guitart exact squares involvi... |
12,093 | lean_file_chunk | 7b7149374bff1061e69196f3446c60361a0afa0c83d6d47fad8c56f6ab4a8d36 | 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.Final
public import Mathlib.CategoryTheory.Functor.TwoSquare
/-!
# Guitart exact squares
Given four functors `T`, `L`, `R`... |
4,666 | lean_file_chunk | 43b071e5f3054775b3b7c2edccc313cba04d2352c8535a3575ae42014ccbb4da | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne, Paul Lezeau
-/
module
public import Mathlib.CategoryTheory.FiberedCategory.HomLift
public import Mathlib.CategoryTheory.Functor.Const
/-!
# Fibers of functors
In this fil... |
13,562 | lean_file_chunk | e1950e96c584075211c2e3cf6941ad5dccf0d455df18aa66bf7001b34fb6e427 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne
-/
module
public import Mathlib.CategoryTheory.FiberedCategory.HomLift
/-!
# Co-Cartesian morphisms
This file defines co-Cartesian resp. strongly co-Cartesian morphisms wit... |
14,813 | lean_file_chunk | 7118ecbb66e48ea93b66cc104df1ed5a4a6b8ef9842569c53ef8abd7787189ce | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Lezeau, Calle Sönne
-/
module
public import Mathlib.CategoryTheory.FiberedCategory.HomLift
/-!
# Cartesian morphisms
This file defines Cartesian resp. strongly Cartesian morphisms... |
10,025 | lean_file_chunk | 5e44c716f575fe40fceb6920f99d3e2ff3514953cce64bd80c0bb20c01b195da | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Lezeau, Calle Sönne
-/
module
public import Mathlib.CategoryTheory.FiberedCategory.HomLift
public import Mathlib.CategoryTheory.Bicategory.Strict.Basic
public import Mathlib.Categor... |
7,444 | lean_file_chunk | c9433673d2b1195cbe6ba0ea9f3589c86ab4a51b6e0a9e7157e45693d43d7e57 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Paul Lezeau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Lezeau, Calle Sönne
-/
module
public import Mathlib.CategoryTheory.FiberedCategory.Cartesian
/-!
# Fibered categories
This file defines what it means for a functor `p : 𝒳 ⥤ 𝒮` ... |
5,095 | lean_file_chunk | 5777d25b171037af1acd87902c0931ca4688acf0d7945bcf8827feb4bf3816e8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne, Fernando Chu, Christian Merten
-/
module
public import Mathlib.CategoryTheory.Bicategory.Grothendieck
public import Mathlib.CategoryTheory.FiberedCategory.HasFibers
/-!
# T... |
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