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 |
|---|---|---|---|---|---|
9,472 | lean_file_chunk | 19071acff30f365941160405b9af5068a77e239c4c8afb8f80a84dd2d1bb0507 | 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.Fiber
public import Mathlib.CategoryTheory.FiberedCategory.Fibered
/-!
# Fibers of functors
In ... |
10,898 | lean_file_chunk | cd4760939d7cfd466494f5171a17bcd502967fbba7fa6ae8d07be85bf49e86e9 | 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.Functor.Category
public import Mathlib.CategoryTheory.CommSq
/-!
# HomLift
Given a functor `p : 𝒳 ⥤ 𝒮`, this ... |
865 | lean_file_chunk | da06558f1ce3b876a97b31522392a7bf3b3abb685a9222dbb5dc43f3d49f26a8 | 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.Center.Preadditive
public import Mathlib.Algebra.Ring.NegOnePow
/-!
# Powers of `-1` in the center of a preadditive category
-/
... |
3,338 | lean_file_chunk | 2a1bdb3fe0a25b01049f17aebadae6d982f7b9c49b8c5e586f8acdb96e6bf570 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Preadditive.FunctorCategory
public import Mathlib.CategoryTheory.Linear.Basic
public import Mathlib.CategoryTheory.Center.Preadditi... |
773 | lean_file_chunk | 944dbd9a3e80560e357e1e9775fddbd847da6d02afcf72d11863173e3c1ad852 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Preadditive.FunctorCategory
public import Mathlib.CategoryTheory.Center.Basic
/-!
# The center of an additive category
-/
public... |
2,782 | lean_file_chunk | fd005e09aa18cf594b7a09eae9cdaa8f0af6de6698ef52e37607255b35a36c56 | 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.Endomorphism
/-!
# The center of a category
Given a category `C`, we introduce an abbreviation `CatCenter C` for
the center of th... |
2,836 | lean_file_chunk | b84d509a212752e1fa53411d5dfc258401fd7450a44ca0753e1d412d0f519261 | 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.Center.Preadditive
public import Mathlib.CategoryTheory.Localization.Predicate
public import Mathlib.CategoryTheory.Preadditive.Add... |
3,623 | lean_file_chunk | dcb3fb99e55aaa4255f15b7b815c7f3d40e71969e556a47c5ba2b25d2e043228 | 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.Category.ModuleCat.Basic
public import Mathlib.CategoryTheory.Linear.Basic
public import Mathlib.CategoryTheory.Preadditive.Yoneda.B... |
4,431 | lean_file_chunk | 89082c2736968c4b75f9c86b14deae9108d0c1d7d66402164ae508387b318882 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
public import Mathlib.CategoryTheory.Linear.Basic
public import Mathlib.Algebra.Module.LinearMap.... |
6,624 | lean_file_chunk | c81b4cc83c30c427ab5bb165decf49264018cbfea092e2a5d9959c372b9341d7 | 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.Algebra.Defs
public import Mathlib.Algebra.Module.TransferInstance
public import Mathlib.Algebra.Group.Invertible.Defs
public import... |
1,796 | lean_file_chunk | 70e0c43b302fc6459b22a681911c64733ca3e098174c5a15c8528620d663c925 | 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.Preadditive.FunctorCategory
public import Mathlib.CategoryTheory.Linear.Basic
/-!
# Linear structure on functor categories
... |
11,954 | lean_file_chunk | 2d1e143ed7a9d4420e84652cea7901806c9fe91f56e0656a532f1e4bf9bf73ab | 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, Floris van Doorn
-/
module
public import Mathlib.CategoryTheory.EqToHom
public import Mathlib.CategoryTheory.Pi.Basic
/-!
# Discrete categories
We define... |
3,210 | lean_file_chunk | c32b0f6f4aa4a9ad6dc6607c34cd25cab2f439c584c80644dab36482e0740f99 | 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.Discrete.Basic
public import Mathlib.CategoryTheory.Sums.Basic
public import Mathlib.CategoryTheory.Products.Basic
/-! # S... |
1,831 | lean_file_chunk | d861b8b35fdc1a5859e9b34d3352622ced8c1d706d7ab0a3289dd5e15d0dc709 | 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.Discrete.Basic
public import Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
/-!
# Structured arrows when the target category i... |
5,132 | lean_file_chunk | 93c4a825ff1072333f0804ceea8a23515239dad937b8ce67c3f54992aa059b6d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Idempotents.Karoubi
/-!
# Biproducts in the idempotent completion of a preadditive category
In this file, we define an instance ... |
6,644 | lean_file_chunk | 529c67732c0d7d9212355861003cfbcdecbe4216682651bd7bd477638b1b6139 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.Algebra.Homology.Additive
public import Mathlib.CategoryTheory.Idempotents.Karoubi
/-!
# Idempotent completeness and homological complexes
This ... |
918 | lean_file_chunk | c6d0316eaa76a3746a032643be49eed7346f574804535f98826079e1d1e0378c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.AlgebraicTopology.SimplicialObject.Basic
public import Mathlib.CategoryTheory.Idempotents.FunctorCategories
/-!
# Idempotent completeness of cat... |
10,542 | lean_file_chunk | 1e448d5308f67edc126fe55efbcfb2e76cce9b59ba09dc5808ee7c627216b59b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Idempotents.Karoubi
/-!
# Extension of functors to the idempotent completion
In this file, we construct an extension `functorExte... |
9,704 | lean_file_chunk | ca74b145bdc45543f9e89c375816ae2ac47afae6fa663848259c1377d0ccf54c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Idempotents.Basic
public import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
public import Mathlib.CategoryTheory.Equivalence... |
7,157 | lean_file_chunk | 0f248e215c9e7b9c941483fcd07184cb5f012ddbd7f7a66694c1a0d86ab69053 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Abelian.Basic
/-!
# Idempotent complete categories
In this file, we define the notion of idempotent complete categories
(also kno... |
5,108 | lean_file_chunk | da17e405053b5098dcdbf56425082ca5c1a0dac40e7c1b87142d048c3936e1f5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Idempotents.Karoubi
/-!
# Idempotent completeness and functor categories
In this file we define an instance `functor_category_isI... |
2,230 | lean_file_chunk | bdface6cbfa30821a68e5ccca79ec55e729a21c52971e3424920a549f0cab9cd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Idempotents.Karoubi
/-!
# Idempotence of the Karoubi envelope
In this file, we construct the equivalence of categories
`KaroubiKa... |
5,662 | lean_file_chunk | a9c9455134642c724b652e39b8ad6b2353598bd06401163374a880016a34a384 | 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.Center.Basic
public import Mathlib.CategoryTheory.Shift.CommShift
/-!
# Twisting a shift
Given a category `C` equipped with a shi... |
12,813 | lean_file_chunk | d46272d325db9e7d227049e7aa73279556fb5759d441b83e2443715789893466 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Shift.Adjunction
public import Mathlib.CategoryTheory.Preadditive.Opposite
/-!
# The (naive) shift on the opposite category
If `C... |
23,967 | lean_file_chunk | c1f9dc0fce8dc9f2aeb8633639e1ff1f9d799d48952821ae3e1a5be06aef08a7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Shift.Basic
public import Mathlib.CategoryTheory.NatIso
/-!
# Functors which commute with shifts
Let `C` and `D` be two categorie... |
2,204 | lean_file_chunk | d15cb7ac1de7e7d36047584fcc44e9c6d993dd7c75114034371a9654a27d5e82 | lean_source_file | pkg_mathlib_source_file_chunks | simp [commShiftIso_comp_hom_app, show F.commShiftIso a = OfComp.iso e a from rfl,
← Functor.map_comp]
end CommShift
end Functor
/--
Assume that we have a diagram of categories
```
C₁ ⥤ D₁
‖ ‖
v v
C₂ ⥤ D₂
‖ ‖
v v
C₃ ⥤ D₃
```
with functors `F₁₂ : C₁ ⥤ C₂`, `F₂₃ : C₂ ⥤ C₃` and `F₁₃ : C₁ ⥤ C₃` on the... |
6,625 | lean_file_chunk | dbb640f4ffef2882942c8fb24cf602999e8bc0ca28b7cde7a0ec71191275fa03 | 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.Triangulated.Opposite.Basic
public import Mathlib.CategoryTheory.Shift.ShiftedHom
/-! Shifted morphisms in the opposite category
... |
10,322 | lean_file_chunk | 426bdc159e28b749abef9e633cbc29373ec0b00fc75b6176ffcb9f80d0d9c065 | 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.Shift.CommShift
/-!
# Functors from a category to a category with a shift
Given a category `C`, and a category `D` equipped with ... |
1,802 | lean_file_chunk | c913910c8d751f52a6e07c7ef8f9aaea883a06396daae5dca4f4596895aca276 | 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.Shift.CommShift
public import Mathlib.CategoryTheory.Localization.Linear
/-!
# Localization of the linearity of the shift functors... |
23,985 | lean_file_chunk | e48c23de7221429eed296c82e62b3a7f559155d68d87304d0f30cd77d3fad977 | 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, Johan Commelin, Andrew Yang, Joël Riou
-/
module
public import Mathlib.Algebra.Group.Basic
public import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero
public import ... |
8,512 | lean_file_chunk | 916ec7fa8fcf6a0d4e9e4108a759c2bae7114f615eecf8ebb59be1c980bd3d3e | lean_source_file | pkg_mathlib_source_file_chunks | shiftFunctorComm C i i = Iso.refl _ := by
rw [shiftFunctorComm_eq C i i (i + i) rfl, Iso.symm_self_id]
lemma shiftFunctorComm_symm (i j : A) :
(shiftFunctorComm C i j).symm = shiftFunctorComm C j i := by
ext1
dsimp
rw [shiftFunctorComm_eq C i j (i + j) rfl, shiftFunctorComm_eq C j i (i + j) (add_comm j i)]... |
6,183 | lean_file_chunk | c06259bca40469a6725afd6fec7d5f71570a45765d13c4f651a6da43e4fa369e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Shift.CommShift
public import Mathlib.CategoryTheory.Shift.Induced
public import Mathlib.CategoryTheory.Quotient
/-!
# The shift o... |
11,958 | lean_file_chunk | 7c68966e2c9f179ed90ce2e540c8a2e50ba4f97c6d7f1e147c7afcccc58adda7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Shift.Basic
public import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
/-! Sequences of functors from a category equipped wi... |
12,274 | lean_file_chunk | a2f04bf9cdacadd7ad31d91543e6ffc193c46ac095c4e32493bff8efe60a7301 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Shift.Induced
public import Mathlib.CategoryTheory.Localization.HasLocalization
public import Mathlib.CategoryTheory.Localization.L... |
13,690 | lean_file_chunk | c4f1c53f8f3bb48f339956ccaad87180a0016ddb0ca9e0db37d9ee0ebdf28d1e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Shift.Adjunction
public import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
/-!
# The pullback of a shift by a monoid morphi... |
9,900 | lean_file_chunk | f2482a6163f4219548b2791a8d0682e37aae7cc182dcc7265c2646f6b7e319bf | 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.Shift.CommShift
public import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
public import Mathlib.CategoryTheory.Linear.Linear... |
23,935 | lean_file_chunk | 4bdbe91d6ca20ee2ad01cc1af4f9ffcfd6ca80a4cb71911ebbf575f832034390 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Sophie Morel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sophie Morel, Joël Riou
-/
module
public import Mathlib.CategoryTheory.Shift.CommShift
public import Mathlib.CategoryTheory.Adjunction.Mates
public import Mathlib.Tactic.CategoryTheory.... |
2,985 | lean_file_chunk | bf259dd130808444f2824b7adbb2c83a6f2caa1df8ff48723ad10ca7ad1fe7d7 | lean_source_file | pkg_mathlib_source_file_chunks | The forward functor of the identity equivalence is compatible with shifts.
-/
instance : (Equivalence.refl (C := C)).functor.CommShift A :=
inferInstanceAs <| (𝟭 C).CommShift A
/--
The inverse functor of the identity equivalence is compatible with shifts.
-/
instance : (Equivalence.refl (C := C)).inverse.CommShift ... |
9,166 | lean_file_chunk | a693c9b4a3b8ff3aed705727276cc7d1f6b166b6fcaabf61e0be6d8e090db26a | 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.Center.NegOnePow
public import Mathlib.CategoryTheory.Linear.LinearFunctor
public import Mathlib.CategoryTheory.Shift.Twist
public ... |
6,106 | lean_file_chunk | 840be4d73718a1cfb984e811149a9602a7ae820c9ac8c9bdf1e93462173d7954 | 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.Shift.CommShift
public import Mathlib.CategoryTheory.Shift.ShiftSequence
/-! # Induced shift sequences
When `G : C ⥤ A` is a func... |
9,906 | lean_file_chunk | 498548be288d40774fec5d48054ad288c6c6b81c9be06fdd9e2f1b1aafbb3c8f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Shift.CommShift
/-!
# Shift induced from a category to another
In this file, we introduce a sufficient condition on a functor
`F ... |
5,154 | lean_file_chunk | 2f4a854ac42e77ada11fdf724512ae320ea31f288b862fb77bc7dd716f5675cc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jack McKoen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jack McKoen, Joël Riou
-/
module
public import Mathlib.CategoryTheory.MorphismProperty.Limits
public import Mathlib.CategoryTheory.MorphismProperty.Retract
public import Mathlib.Category... |
5,937 | lean_file_chunk | 2e5894d654e2ecf6d5ab0e89d540c959e2eb327480cb745a0c337d2f18220b55 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Functor.ReflectsIso.Basic
public import Mathlib.CategoryTheory.MorphismProperty.Basic
/-!
# Morphism properties that are inverted ... |
4,203 | lean_file_chunk | 42dd5f68a0f6000dc11046e8e09a4c2db8779fd186ca75d2a5abf3f4fc2b122a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jack McKoen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jack McKoen
-/
module
public import Mathlib.CategoryTheory.Retract
public import Mathlib.CategoryTheory.MorphismProperty.Basic
/-!
# Stability under retracts
Given `P : MorphismPropert... |
17,486 | lean_file_chunk | c99b57b27e19e13de31f2a3b4f3bd999b4ab10d0352eaefc7e5a7cdb55e9ad47 | 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, Joël Riou
-/
module
public import Mathlib.CategoryTheory.MorphismProperty.Basic
/-!
# Compatibilities of properties of morphisms with respect to composition
Given `P : Mor... |
23,974 | lean_file_chunk | 2558f25a30df360c24ef8fa6aea5aae88fd5cd1fd0cb76b264afdd6468ec630d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.CategoryTheory.Comma.Over.Basic
public import Mathlib.CategoryTheory.MorphismProperty.Composition
public import Mathlib.CategoryTheo... |
6,857 | lean_file_chunk | 7085dbbdb360656e3ceea8bd8e0424ea7ff6a69bfcdbb87eb1c7af3850ae61a5 | lean_source_file | pkg_mathlib_source_file_chunks | /-- Make a morphism in `P.Over Q X` from a morphism in `T` with compatibilities. -/
@[simps hom]
protected def Over.homMk {A B : P.Over Q X} (f : A.left ⟶ B.left)
(w : f ≫ B.hom = A.hom := by cat_disch) (hf : Q f := by trivial) : A ⟶ B where
__ := CategoryTheory.Over.homMk f w
prop_hom_left := hf
prop_hom_rig... |
8,928 | lean_file_chunk | 6b4734008e687103f5640bc9dd5236b42fcdca9af12130157846297b7ff9f78e | 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.Limits
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equalizer
/-!
# Descent of morph... |
2,059 | lean_file_chunk | e3f387177a25ebc91b6c64be38df141e8f44068502bd2a6876d600c010b97f1e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.MorphismProperty.Basic
public import Mathlib.Logic.Small.Basic
/-!
# Small classes of morphisms
A class of morphisms `W : Morphis... |
20,626 | lean_file_chunk | 141d8ac0a7dd28a0c881328246952d99c813a6df2e4936c126bafc3e769ae345 | 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.Comma.Arrow
public import Mathlib.Order.CompleteBooleanAlgebra
/-!
# Properties of morphisms
We provide the basic framework f... |
8,374 | lean_file_chunk | 1bd416377c2912ab1d782c8dce593c8395cbd5ba50f9a8e1660ecffba99c3d0d | 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, Andrew Yang
-/
module
public import Mathlib.CategoryTheory.Sites.Hypercover.Zero
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equalizer
public impor... |
2,756 | lean_file_chunk | d5a5180fdf7928f1a2f8a9daf4a86a1d1c9f4fa2c9ab2697834006c7252dc8d6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.MorphismProperty.Basic
public import Mathlib.CategoryTheory.Quotient
/-!
# Classes of morphisms induced on quotient categories
Le... |
1,941 | lean_file_chunk | 35e9ab1fe98e87ece382dd95ffac2e80ae27e8d2bc0f313028591549bf5bc67e | 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.SetTheory.Cardinal.HasCardinalLT
public import Mathlib.CategoryTheory.MorphismProperty.Basic
/-!
# Properties of morphisms that are bounded by a ... |
2,470 | lean_file_chunk | 87763688a951e750c10071f44a3e4a25aa67dbf3edb5410b7500591a5a888086 | 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.Factorization
public import Mathlib.CategoryTheory.MorphismProperty.LiftingProperty
/-!
# The retract argument
L... |
3,264 | lean_file_chunk | 5a1ee629f167049f0bf7ddc54d4a5ad856691c6904881195131c6f5836880954 | 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.Sites.MorphismProperty
public import Mathlib.CategoryTheo... |
10,052 | lean_file_chunk | 0913b9cc4a84f59371fdac0fe57a3825bfb0f7ca4d7cc659199a9871d839149a | 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.Comma.LocallySmall
public import Mathlib.CategoryTheory.Limits.Preserves.Over
public import Mathlib.CategoryTheory.Mo... |
9,007 | lean_file_chunk | d35236a09f4162dcbe4179a804837a52d04dd06e7a93d6fe0c9fdb7bd3f3edc0 | 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.Basic
/-!
# The factorization axiom
In this file, we introduce a type-class `HasFactorization W₁ W₂`, which, giv... |
2,250 | lean_file_chunk | 04c55633a0aa558099d33fe202f52e80de3a825a59c8496f2b6c851bd2668c51 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
module
public import Mathlib.CategoryTheory.MorphismProperty.Limits
/-!
# Morphism properties from object properties
Given two object properties `P` and `Q`, we ... |
2,169 | lean_file_chunk | 8709726e76486784ffaa4f50050c2e301e2bff657855c3ba7ae8d16e9fd3b001 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.MorphismProperty.RetractArgument
/-!
# Weak factorization systems
In this file, we introduce the notion of weak factorization sys... |
23,981 | lean_file_chunk | f9b43ba19c3222f165d36e7f9c5001a6fce65607e0b8871979cfefa629629566 | 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, Joël Riou, Ravi Vakil
-/
module
public import Mathlib.CategoryTheory.MorphismProperty.Limits
/-!
# Relatively representable morphisms
In this file we define and develop b... |
5,375 | lean_file_chunk | 1dcb8c33aad55b9509bed1e6642a5dd9c4b79cc6d9e32bebb8d2362dea2bee88 | lean_source_file | pkg_mathlib_source_file_chunks | For an object `X` in a category `D`, if the diagonal morphism `X ⟶ X × X` is relatively
representable, then every morphism of the form `F.obj a ⟶ X` is relatively representable with
respect to `F`.
-/
lemma of_diag {X : D} (h : F.relativelyRepresentable (Limits.diag X))
⦃a : C⦄ (g : F.obj a ⟶ X) : F.relativelyRepre... |
23,985 | lean_file_chunk | 41d649b0055b13e2f19102619f8c95520d4225c6626f336615b64ea825148e13 | 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, Joël Riou
-/
module
public import Mathlib.CategoryTheory.Limits.Final
public import Mathlib.CategoryTheory.Limits.Connected
public import Mathlib.CategoryTheory.Filtered.Con... |
18,348 | lean_file_chunk | 62adbb588f9714272c0339ab6e255078e9738f21cab213230eb524062bab7e9a | lean_source_file | pkg_mathlib_source_file_chunks | let e₂ := Arrow.rightFunc.mapIso e
have fac : e₁.hom ≫ g = h₁.desc (Cocone.mk _ (f ≫ c₂.ι)) ≫ e₂.hom := e.hom.w
let c₁' : Cocone X₁ := { pt := Y₁, ι := c₁.ι ≫ (Functor.const _).map e₁.hom }
let c₂' : Cocone X₂ := { pt := Y₂, ι := c₂.ι ≫ (Functor.const _).map e₂.hom }
have h₁' : IsColimit c₁' := IsColimi... |
17,171 | lean_file_chunk | f9d14de646b64b45c93496b58cbb107611d346d83310f398dde7a20c68590472 | 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.Connected
public import Mathlib.CategoryTheory.Limits.Shapes.Preorder.TransfiniteCompositionOfShape
public import Mathlib.Ca... |
5,082 | lean_file_chunk | 04d122e14e825d1bea1b73d1ddb210a9abf71d71d24402a9ffe348ddb546bffd | 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.ConcreteCategory.Forget
public import Mathlib.CategoryTheory.MorphismProperty.Composition
public import Mathlib.CategoryTheory.... |
4,793 | lean_file_chunk | cebfc72a83f2f578e98a39ffd59d9cc4e559da0fec9d6d2f356d57c36abdc171 | 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.FunctorCategory.EpiMono
public import Mathlib.CategoryTheory.MorphismProperty.Retract
public import Mathlib.CategoryTheory.M... |
14,986 | lean_file_chunk | a49d97af5ae71f304cae3e67063770d9b4a644af3d4f8049821da33dcd1534ae | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.CategoryTheory.MorphismProperty.Comma
public import Mathlib.CategoryTheory.Comma.Over.Pullback
public import Mathlib.CategoryTheory.... |
10,125 | lean_file_chunk | 4bc09296eb1223278d308412f24b447abb5f9e7be307ef48727aab5c3e70cbb2 | 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.SmallObject.WellOrderInductionData
public import Mathlib.CategoryTheory.MorphismProperty.LiftingProperty
public import Mathlib.Cate... |
6,002 | lean_file_chunk | d5d6f1e1577447253e174360556936e2d09ed5ef9c45ef03fbccfc6e22db7ed7 | 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.SmallObject.Iteration.Nonempty
public import Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition
public import Mathlib.C... |
13,452 | lean_file_chunk | a7a947c54c8f8fa371d10cfc20005b16ff34ef09923934dae4d75ee51c7e97de | 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.Products
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
public import Mathlib.AlgebraicTopol... |
10,981 | lean_file_chunk | 5face95e17308237400b36bc581f70a950e1712ea0608da89122f4b6bed615c3 | 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.Category.Preorder
public import Mathlib.CategoryTheory.Functor.Category
public import Mathlib.CategoryTheory.Types.Basic
public imp... |
6,258 | lean_file_chunk | c9ee328a2b50899d8028cb17c67156db8a537a1687513b38584a881efa727abd | 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.SmallObject.IsCardinalForSmallObjectArgument
/-!
# The small object argument
Let `C` be a category. A class of morphisms `I : Mor... |
22,334 | lean_file_chunk | 650f905748186f372221229d807d46ae2bfc0056171bf2d6c1bbc9e0a4fb0d8d | 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.SmallObject.Construction
public import Mathlib.CategoryTheory.SmallObject.TransfiniteIteration
public import Mathlib.CategoryTheory... |
1,910 | lean_file_chunk | e62d908658537a565e1ae435598acb0bbcb20f3aeece95f5ac8c56e32c06b452 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.EffectiveEpi.Preserves
public import Mathlib.CategoryTheory.EffectiveEpi.Coproduct
public import Mathlib.CategoryTheo... |
2,517 | lean_file_chunk | 891571b6f4ca637e916f23d2ad05601b5c02f36bd6804bdeeaeb8b53407bde22 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.EffectiveEpi.Basic
/-!
# Effectively enough objects in the image of a functor
We define the class `F.EffectivelyEno... |
5,411 | lean_file_chunk | b5da08331cc08f202394cbcfce36596792fb0ef47e7010c7c0133b83c67526fb | 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.EffectiveEpi.Basic
/-!
# Composition of effective epimorphisms
This file provides `EffectiveEpi` instances for cert... |
11,814 | lean_file_chunk | 1c965f900819030bb12c151462639a52f1baedeebb5e0a9a67c237a0cdfa0f18 | 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.EffectiveEpi.Comp
public import Mathlib.CategoryTheory.Limits.Shapes.RegularMono
public import Mathlib.CategoryTheory... |
12,236 | lean_file_chunk | ce4383d17fe7f0db7e710768427ffc8ff0a72bf195c7fadb4df88c62c9196347 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Products
/-!
# Effective epimorphisms
We define the notion of effective epimorphism and effective epimorphic fami... |
479 | lean_file_chunk | 49aa22d1962599e5f98fa56b3bd0a86b9f863dee336191f97eb5e0f3bbbc60c1 | 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 -- shake: keep-all
public import Mathlib.CategoryTheory.Category.Init
public import Mathlib.Data.Finset.Attr
public import Mathlib.Tactic.Common
public im... |
5,523 | lean_file_chunk | d1bd1d16fddb774aa3973d7b7141373a6778101bf4c7337bdc4cd15d3f06fe6a | 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.EffectiveEpi.Basic
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
public import Mathlib.Tact... |
8,749 | lean_file_chunk | cb0a0fdf4b1069f3c2d73555376cc8e6f8b86a38cc5e871a984732498e91243a | 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.FunctorCategory.Basic
public import Mathlib.CategoryTheory.Limits.Types.Yoneda
public import Mathlib.Cat... |
1,511 | lean_file_chunk | 2c2aed2991d67b26c24776626a9f4a3ab8fb5cc580be37852eea13e203a63299 | 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.Types.Colimits
/-!
# Concrete description of (co)... |
23,988 | lean_file_chunk | 616ea5f7f095fe25fb20b6dc929327c72671d6d2d8d2cec8cf8fc004f734a171 | 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: Reid Barton, Mario Carneiro, Kim Morrison, Floris van Doorn
-/
module
public import Mathlib.CategoryTheory.Limits.IsLimit
public import Mathlib.CategoryTheory.Category.ULift
public impo... |
23,963 | lean_file_chunk | 52e5403a6e165ea04231e65a744265f22498a3f35377a45a2d347fc415b0ad05 | lean_source_file | pkg_mathlib_source_file_chunks | lemma HasLimitsOfShape.of_essentiallySmall
[HasLimitsOfSize.{v₁, u₁} C] (J : Type u₂) [Category.{v₂} J]
[EssentiallySmall.{u₁} J] [LocallySmall.{v₁} J] :
HasLimitsOfShape J C := by
have := HasLimitsOfShape.of_small.{v₁, u₁} C (SmallModel.{u₁} J)
exact hasLimitsOfShape_of_equivalence (equivSmallModel.{u₁... |
2,923 | lean_file_chunk | 7c5323c231506171c815a331ed55df4ef3d0738451d82ade61521c13a3f3d4f0 | lean_source_file | pkg_mathlib_source_file_chunks | HasColimitsOfSize.{v₁, u₁} C := hasColimitsOfSizeOfUnivLE.{max v₁ v₂, max u₁ u₂} C
instance (priority := 100) hasSmallestColimitsOfHasColimits [HasColimits C] :
HasColimitsOfSize.{0, 0} C :=
hasColimitsOfSizeShrink.{0, 0} C
end Colimit
section Opposite
/-- If `t : Cone F` is a limit cone, then `t.op : Cocone ... |
4,599 | lean_file_chunk | 74382ee731ef892e33e9387f664b5bd4be9cfe9c42c6a2e6d4f18ed3fb017f73 | 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.Limits.Types.Colimits
public import Mathlib.CategoryTheory.Limits.Types.Limits
public import Mathlib.CategoryTheory.Functor.C... |
1,575 | lean_file_chunk | da60e558d15d803f34ba2bb9393a75de2ee677e8fb212a14434a30dc8929b962 | 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.Products
public import Mathlib.CategoryTheory.EssentiallySmall
/-!
# Limits over essentially small indexing ... |
7,182 | lean_file_chunk | 8b1ce42b13ea61568b63591ef4c647efaa84c34579e5dd62a88192bbb919bd1c | 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.Connected
public import Mathlib.CategoryTheory.Limits.Final
/-!
# (Co)limit presentations
Let `J` and `C` be... |
117 | lean_file_chunk | 1d6e23096a07e232e494ef8854f35c24c1e150b52e8a407289b8d10052c46343 | lean_source_file | pkg_mathlib_source_file_chunks | module
public import Mathlib.CategoryTheory.Limits.FormalCoproducts.Basic
deprecated_module (since := "2026-02-09") |
3,402 | lean_file_chunk | 67fed546bd318cf6b01f84dd36ade81325d264357e05bec9af62fba785a418ad | 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.IsPullback.Defs
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono
/-!
# Relation between mon... |
23,965 | lean_file_chunk | cc8a9dbe045b4db228e3007211ad4e33763654821fb4167e2197e5c9244d04b6 | 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.Limits.HasLimits
public import Mathlib.CategoryTheory.Products.Basic
public import Mathlib.CategoryTheory.Functor.Currying
pu... |
5,533 | lean_file_chunk | a9b63a87e36ac35d903f3625df892a96d39d8558f9ecd52a34d2ff79131b7ec1 | lean_source_file | pkg_mathlib_source_file_chunks | trans limit (uncurry.obj ((@curry J _ K _ C _).obj G))
· apply HasLimit.isoOfNatIso i
· exact limitUncurryIsoLimitCompLim ((@curry J _ K _ C _).obj G)
set_option backward.isDefEq.respectTransparency false in
@[simp, reassoc]
theorem limitIsoLimitCurryCompLim_hom_π_π {j} {k} :
(limitIsoLimitCurryCompLim G).hom ... |
15,447 | lean_file_chunk | 1201e645567de56d8a59ffc43072e7bca662adfbd475eccb52854938fa72204e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.CategoryTheory.Limits.Opposites
public import Mathlib.CategoryTheory.Limits.Preserves.Limits
public import Mathlib.CategoryTheory.Li... |
11,221 | lean_file_chunk | d92d83ceeb98b7f9ba0d2f96cff7f91b976e22d1bf811c0f4b1e9d1093f2b6a1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Monoidal.FunctorCategory
public import Mathlib.CategoryTheory.Monoidal.ExternalProduct.Basic
public import Mathlib.Category... |
2,622 | lean_file_chunk | 1bd76813be65fd5cb6d9037ba00dcbc664eaf3b8e1ae105a4c5078554551fe98 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Fernando Chu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fernando Chu
-/
module
public import Mathlib.CategoryTheory.Adjunction.Limits
public import Mathlib.CategoryTheory.Skeletal
/-!
# (Co)limits of the skeleton of a category
The skeleton... |
5,557 | lean_file_chunk | aece9971b95a7805c70824886341b99038e4a79f40658eb17a7f9c563d902339 | 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.Filtered.Basic
public import Mathlib.CategoryTheory.Limits.HasLimits
public import Mathlib.CategoryTheory.Limits.Types.Yone... |
1,630 | lean_file_chunk | 0ca62aa488e457892af77accdfbd16fece23399c7bfd70b0f1bc9f6a67a3d9e9 | 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.PUnit
public import Mathlib.CategoryTheory.Limits.HasLimits
/-!
# `Discrete PUnit` has limits and colimits
Mostly for the s... |
23,974 | lean_file_chunk | 5d209dd629207f7acaf65840d53d3220995b2ec1ea18ac1a9e1159ed40156765 | 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, Joël Riou
-/
module
public import Mathlib.CategoryTheory.Comma.Presheaf.Basic
public import Mathlib.CategoryTheory.Functor.KanExtension.Adjunction
public import Mathlib.Ca... |
14,364 | lean_file_chunk | c5cf51a0a2a097bf0837844952b1954ad9e9498e2c9b8e6382b0f13fe16f0085 | lean_source_file | pkg_mathlib_source_file_chunks | hom_ext_uliftYoneda.{max w v₂} (fun X p ↦ uliftYonedaEquiv.injective (by
rw [← assoc p f, uliftYonedaEquiv_ι_presheafHom, ← assoc,
uliftYonedaEquiv_comp, uliftYonedaEquiv_ι_presheafHom,
Functor.map_comp]
dsimp))
variable [∀ (P : Cᵒᵖ ⥤ Type max w v₁ v₂), F.op.HasLeftKanExtension P]
/-- Given functo... |
17,761 | lean_file_chunk | 3697b5b82636d36734b42ec029cae72d9e5ab8163159c80ca5ccafc5582c4657 | 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.Limits.ColimitLimit
public import Mathlib.CategoryTheory.Limits.Preserves.FunctorCategory
public import Mathlib.CategoryTheor... |
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