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 |
|---|---|---|---|---|---|
23,931 | lean_file_chunk | e8301cf91b9b4cce261a3f97e65efb9c0b9d3711d76dfbb1e43dfcc968e7b563 | 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.Functor.Const
public import Mathlib.CategoryTheory.Discrete.Basic
public import Mathlib.Cat... |
8,644 | lean_file_chunk | a72a45c0b5df66144d44aac9ee43b35d36c1313270667115b3167aa5014d6ce5 | lean_source_file | pkg_mathlib_source_file_chunks | noncomputable def mapConeInvMapCone {F : J ⥤ D} (H : D ⥤ C) [IsEquivalence H] (c : Cone F) :
mapConeInv H (mapCone H c) ≅ c :=
(Limits.Cone.functorialityEquivalence F (asEquivalence H)).unitIso.symm.app c
/-- `functoriality F _ ⋙ postcompose (whisker_left F _)` simplifies to `functoriality F _`. -/
@[to_dual (at... |
23,909 | lean_file_chunk | 0f5109fc9b810994914ed20debf736edc49d2add9be9c00be27cc435da4e3864 | 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, Jakob von Raumer
-/
module
public import Mathlib.CategoryTheory.Category.Cat.AsSmall
public import Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
public import Mathlib... |
23,954 | lean_file_chunk | 6454529a6f68d19fcc2f2088ad8370c4e5fdf6e3f8da2f176b9b954ad34fdab1 | lean_source_file | pkg_mathlib_source_file_chunks | rw [← a, Functor.map_comp, ← Functor.comp_map, ← Category.assoc, ← Category.assoc,
c.w, z, Category.assoc]
· rw [← Functor.map_comp] } }
map f := { hom := f.hom }
set_option backward.isDefEq.respectTransparency false in
/-- Alternative equational lemma for `(extendCone c).π.app` in case a... |
4,847 | lean_file_chunk | 6db8a41eac3c49b82fe5444d70c70d4c9b73c8e02c670202fdb0fd83ad12a411 | lean_source_file | pkg_mathlib_source_file_chunks | HasColimit.isoOfNatIso (fiberwiseColimitMapCompEquivalence α H) ≪≫ colimitFiberwiseColimitIso _
convert Iso.isIso_hom i
apply colimit.hom_ext
intro X
simp [i, fiberwiseColimitMapCompEquivalence]
set_option backward.isDefEq.respectTransparency false in
/-- The functor `Grothendieck.map α` for a natural transfor... |
12,834 | lean_file_chunk | 818df9d001c1917b4eae8e2ea3d5a0fccf9abc17d47e2d5031c5f82a57a3a7e5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Comma.Arrow
public import Mathlib.CategoryTheory.Comma.Over.Basic
public import Mathlib.CategoryTheory.Limits.Constructions.E... |
6,396 | lean_file_chunk | ba9b4ad7fb468b9db583408bb050b47fe57a10359df12b4e20b248b8c18677da | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Reid Barton, Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Limits.Comma
public import Mathlib.CategoryTheory.Limits.ConeCategory
public import Mathlib.Ca... |
2,234 | lean_file_chunk | 60d37d03bc09fe194dc4edfca577688f9513ead3c28b63b63e7782d33a24af69 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Products
public import Mathlib.SetTheory.Cardinal.Basic
/-!
# Any small complete category is a preorder
We sh... |
10,288 | lean_file_chunk | 7f637abb6d7aecdce6cb694eaa883d6d462f4bde388034eb52cefa1e4194411e | 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.ConcreteCategory.Forget
public import Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts
public import Mathlib.CategoryT... |
4,382 | lean_file_chunk | 18feb3737d0a9a2a2bd675dca5df82e89b7327f67ef674a117720b1ecbbe19b4 | 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.Pi.Basic
public import Mathlib.CategoryTheory.Limits.HasLimits
/-!
# Limits in the category of indexed families of objects.
... |
16,575 | lean_file_chunk | b8389bacd858bf1b92cd6e54d571ca76c68293dacb6a693b8b55a5319d2ec043 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.CategoryTheory.Adjunction.Comma
public import Mathlib.CategoryTheory.Comma.Over.Basic
public import Mathlib.CategoryTheory.Limits.Preserves.Sh... |
7,077 | lean_file_chunk | 430f992a53d55f8804b56304d40ae4f46827942472d846b92a954e00e42b0f0f | 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.ObjectProperty.LimitsOfShape
public import Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape
/-!
# Limits in full subc... |
23,991 | lean_file_chunk | 40b6920a97fd19271953294710e1a32fc205c3ffe7b2218b8d579c920fff7520 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Functor.ReflectsIso.Basic
public import Mathlib.CategoryTheory.Limits.Preserves.Basic
/-!
# Creating (co)limits
We say that... |
10,254 | lean_file_chunk | e02c656222c2f89e4c051844e3b7e2822340c6fff1d90ad6b6065fac8a808d30 | lean_source_file | pkg_mathlib_source_file_chunks | [CreatesColimitsOfSize.{w, w'} F] [HasColimitsOfSize.{w, w'} D] :
PreservesColimitsOfSize.{w, w'} F where
/-- Transfer creation of limits along a natural isomorphism in the diagram. -/
@[implicit_reducible]
def createsLimitOfIsoDiagram {K₁ K₂ : J ⥤ C} (F : C ⥤ D) (h : K₁ ≅ K₂) [CreatesLimit K₁ F] :
CreatesLimi... |
10,376 | lean_file_chunk | 4e82f8fbcce05c0938aa88f078feab2580ce6d71c18c9cf4255b64dc40302c34 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.CategoryTheory.Limits.Preserves.Finite
public import Mathlib.CategoryTheory.ObjectProperty.CompleteLattice
/-!
# Bundled exact functors
... |
1,402 | lean_file_chunk | 18dafcbcd86077910bd9c30799e514433a35ecc2bef72062914233705379b10f | 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.Lattice
public import Mathlib.CategoryTheory.Limits.Preserves.Basic
public import Mathlib.CategoryTheory.Limits.Types.Filter... |
10,196 | lean_file_chunk | 9b34a6d02f1e9520e1c571f520f608c34cca6af9d4a8033710689e7b4cd94609 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.Logic.Small.Set
public import Mathlib.CategoryTheory.Filtered.Final
public import Mathlib.CategoryTheory.Comma.StructuredArrow.Small
/-!
... |
9,929 | lean_file_chunk | 8f738b575c7dd86bd039a0f03d0feb601821a9935c46b6c9e4cf3abd5e07c530 | 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.Constructions.Over.Basic
public import Mathlib.CategoryTheory.MorphismProperty.OverAdjunction
/-!
# (Co)limit... |
23,986 | lean_file_chunk | c404b38669a4c32d9c6b8b03796584a74085b9858e44102c5c74711971afd706 | 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, Floris van Doorn
-/
module
public import Mathlib.CategoryTheory.Limits.HasLimits
public import Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits
/-!
# Limits in `C` give ... |
3,232 | lean_file_chunk | eb0946302324c70bb458400a10f5d92966b69e5437fb0f126156c575d18bf01c | lean_source_file | pkg_mathlib_source_file_chunks | ⟨fun _ ↦ hasColimit_of_hasLimit_rightOp F, fun _ ↦ inferInstance⟩
lemma hasLimitsOfShape_opposite_iff : HasLimitsOfShape J Cᵒᵖ ↔ HasColimitsOfShape Jᵒᵖ C := by
refine ⟨fun _ ↦ ?_, fun _ ↦ inferInstance⟩
have : HasLimitsOfShape Jᵒᵖᵒᵖ Cᵒᵖ := hasLimitsOfShape_of_equivalence (opOpEquivalence J).symm
exact hasColimit... |
8,422 | lean_file_chunk | e60210bcf52b361d994e155955f07eb5e4691f592275c09faa772e769e01906d | 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.Limits.Shapes.BinaryProducts
public import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
public import Mathlib.C... |
23,969 | lean_file_chunk | 2198539997aee72c2eaff2433a0384a3cdcbc97c895da91d69bb05b6134147cf | 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.Adjunction.Basic
public import Mathlib.CategoryTheory.Limits.Cones
public impo... |
17,907 | lean_file_chunk | 31416e613f8ac488991a65ed73b7ad11a9b69b6a8fa25fe5e1f1d29b75e8bdfa | lean_source_file | pkg_mathlib_source_file_chunks | def uniqueUpToIso {s t : Cocone F} (P : IsColimit s) (Q : IsColimit t) : s ≅ t where
hom := P.descCoconeMorphism t
inv := Q.descCoconeMorphism s
hom_inv_id := P.uniq_cocone_morphism
inv_hom_id := Q.uniq_cocone_morphism
/-- Any cocone morphism between colimit cocones is an isomorphism. -/
theorem hom_isIso {s t... |
23,916 | lean_file_chunk | 287913c9732ec3c25da40b79f55acca2898ea2d96c9c01ccd26a94f818b6f44b | 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.Adjunction.FullyFaithful
public import Mathlib.CategoryTheory.Adjunction.Limits
public import Mathlib.CategoryTheory.Limits.Sha... |
20,640 | lean_file_chunk | b4b085fdd9e3dcd597446c1e1ea8e3d214fe9979ca4538a7db6a898b3c7139fc | lean_source_file | pkg_mathlib_source_file_chunks | refine (h (BinaryCofan.mk (initial.to Y) (𝟙 Y)) (mapPair (initial.to X) (𝟙 Y)) c.inr ?_
(.of_discrete _)).mp ⟨?_⟩ ⟨WalkingPair.right⟩
· ext ⟨⟨⟩⟩ <;> simp
· exact ((BinaryCofan.isColimit_iff_isIso_inr initialIsInitial _).mpr (by
dsimp
infer_instance)).some
theorem BinaryCofan.isPullback_initial_... |
4,832 | lean_file_chunk | 87219805eabe859f12d3627147da92108a032ca4c6d3b42c6aeb1b2944fd0b2d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.CategoryTheory.Limits.Cones
public import Mathlib.CategoryTheory.FinCategory.Basic
public import Mathlib.Data.Finset.Lattice.Lemmas
/-!
# Bic... |
8,238 | lean_file_chunk | 3ab46b90a06bf4a09f06334faf35c158f18b83ddfd643e794be2e50c90d3da5e | 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, Justus Springer
-/
module
public import Mathlib.CategoryTheory.Category.Preorder
public import Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits
public import Mathlib.Cate... |
7,417 | lean_file_chunk | 8e9ed01d4808a00db39f404b65661a5c739b17c2b06b1218a3f30e261cb05aba | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Paul Reichert. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Reichert
-/
module
public import Mathlib.CategoryTheory.Limits.Types.Colimits
public import Mathlib.CategoryTheory.IsConnected
public import Mathlib.CategoryTheory.Limits.Final
pu... |
8,109 | lean_file_chunk | e1d633bfa39d29cc101024e60355198d5f669a201b0fa0976d7914ebca9eb3d3 | 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, Joël Riou, Fernando Chu
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
public import Mathlib.Order.Bounds.Defs
/-!
# (Co)limits in a pr... |
8,178 | lean_file_chunk | a204b0abbe2f0bc5aa3a49077231c62528ab416ab27a0b14ad1f01b28d80305e | 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.Filtered
public import Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Products
public import M... |
4,416 | lean_file_chunk | a70d07f1837e1944fbdb13fe22da8c7bdf9fda6bc15fa9f68a64b4d35f65de87 | 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.Elements
public import Mathlib.CategoryTheory.Limits.Types.Limits
public import Mathlib.CategoryTheory.Limits.Creates
publi... |
6,799 | lean_file_chunk | 8da9bd330652e71c2783903e9d29a188cbab637de55e2437fbd58927252f0d52 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 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.FintypeCat
public import Mathlib.CategoryTheory.Limits.Creates
public import Mathlib.CategoryTheory.Limits.Preserves.... |
4,249 | lean_file_chunk | 2f62e09316af64a8aadb2fcada2b3e2939833bd3d9e96be2663001f5d7f36031 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Comma.Arrow
public import Mathlib.CategoryTheory.FinCategory.Basic
public import Mathlib.CategoryTheory.EssentiallySmall
public imp... |
1,568 | lean_file_chunk | 954cde1ee3ef18c0fe3b653f2cdebf36a17a84084aa6b7d25c4f0e890fd5922a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
public import Mathlib.CategoryTheory.Comma.Over.Basic
public import Mathlib.CategoryTheory.EssentiallyS... |
8,298 | lean_file_chunk | d20072e54905d1a68231e742fd7bd2fe79412724fc8d261e459428c85da99215 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
module
public import Mathlib.CategoryTheory.Functor.KanExtension.Adjunction
public import Mathlib.CategoryTheory.Limits.IsConnected
public import Mathlib.Categor... |
20,595 | lean_file_chunk | 6bc0a9d1a69fe491c84d527749ba3501a34b7881b9dbf7b49ffe399510be3e81 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Johan Commelin, Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Iso
public import Mathlib.CategoryTheory.Functor.Category
public import Mathlib.CategoryTheory.... |
13,402 | lean_file_chunk | 4e8c71227028d782e0fefe9e1f77a875b3642023224ed9d0e9284cf61ced6d25 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.CategoryTheory.Comma.Basic
/-!
# The category of arrows
The category of arrows, with morphisms commutative squares.
We set this up as a ... |
6,663 | lean_file_chunk | 8657a7a376529ac640628d040d970332f586cd066c27040d823b5139042f8042 | 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.Subfunctor.OfSection
/-!
# Subpresheaves that are generated by finitely many sections
Given `F : Cᵒᵖ ⥤ Type w`, `G : Subfunctor F... |
3,429 | lean_file_chunk | 0e9a3549cce23964bf8af2266e9a6fb603c9e8b14792ab5ed5f53eeb05ce5ecf | 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.Subfunctor.Image
public import Mathlib.CategoryTheory.Yoneda
/-!
# The subpresheaf generated by a section
Given a presheaf of typ... |
7,568 | lean_file_chunk | a9aa3ef19e761b2efd542eb4e0275ef8dae03acc73c90f5135e66146a7df24a7 | 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.Subfunctor.Basic
public import Mathlib.CategoryTheory.Limits.FunctorCategory.EpiMono
public import Mathlib.CategoryT... |
7,381 | lean_file_chunk | 4f16a2f17ef4b3d18a9141c3e05779f413f9883d3fbecdc78e67d689e13a0c1e | 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.Elementwise
public import Mathlib.CategoryTheory.Types.Basic
public import Mathlib.Data.Set.Lattice.Image
/-!
# Su... |
2,814 | lean_file_chunk | 2d7bc9b3cd69f017543abd96fe842c1781a8f597318f93da208e71060c6a26cd | 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.Subfunctor.Image
public import Mathlib.CategoryTheory.Subobject.Basic
/-!
# Comparison between `Subfunctor`, `MonoOver` and `Subob... |
2,112 | lean_file_chunk | 97ab093cc10ae6edf57086e91ced9f0076fbfbd07c61e49c67f9a1cb8009edc1 | 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.Subfunctor.Basic
public import Mathlib.CategoryTheory.Sites.IsSheafFor
/-!
# Sieves attached to subpresheaves
Given a subpres... |
5,688 | lean_file_chunk | 28a30c271c40e81e4297b116c899436158e09fcc9a6207cf68d464b2b102e79b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
public import Mathlib.CategoryTheory.Subfunctor.Image
/-!
# The equalizer of two morphisms of functors, a... |
6,075 | lean_file_chunk | c2ec1a124c9c5ea64eba0b8766fa82df8e24f537e1400cc04e20f2e3bbbdff5e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Johannes Hölzl, Reid Barton, Sean Leather, Yury Kudryashov, Anne Baanen,
Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.ConcreteCategory.Basic
public im... |
7,120 | lean_file_chunk | f73546d8ad339ccd17d2e0783bce6414b507548f65f94557a88275871b6971e2 | 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.Constructions.EpiMono
public import Mathlib.CategoryTheory.Limits.Preserves.Basic
public import Mathlib.CategoryTheory.Limit... |
1,681 | lean_file_chunk | 8027f21ab49d01c5309ef6cfe8782e53d660ddad2ea50c2dbf89633cc9bb0efb | 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.ConcreteCategory.Forget
public import Mathlib.CategoryTheory.Functor.ReflectsIso.Basic
/-!
A `forget₂ C D` forgetful functor... |
805 | lean_file_chunk | d79f0c04807abe5d36b36ead6cb25464881e5a2c4dcd072746356682d1961c34 | 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.Tactic.CategoryTheory.Elementwise
public import Mathlib.CategoryTheory.Limits.HasLimits
public import Mathlib.CategoryTheory.Limits.Shapes.Ker... |
8,221 | lean_file_chunk | 72cc34b997cdd09e75bfe22a304c81217e5f80a2d07a5fad9b32bd10ccd679c4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Johannes Hölzl, Reid Barton, Sean Leather, Yury Kudryashov, Anne Baanen,
Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.ObjectProperty.FullSubcategory
... |
2,134 | lean_file_chunk | 9e62301ccea7fdee160d26cf0b52bbae8e1aa487fed481b6d61cad5824ec5799 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Johannes Hölzl, Reid Barton, Sean Leather
-/
module
public import Mathlib.Init
public import Batteries.Tactic.Lint.Misc
/-!
# Bundled types
`Bundled c` provides a unifor... |
1,031 | lean_file_chunk | cbe4bec4c43d7f38061b48635af6cc0e237e3f0f72c02addd000f32d2e7e62dd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Yoneda
public import Mathlib.CategoryTheory.ConcreteCategory.Forget
/-!
# Representable functors in concrete catego... |
337 | lean_file_chunk | d033922dbef590e727e82a022df19f8a4f07fba23c44149dc54a90c0deb12f4d | 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.Category.Init
public import Mathlib.Tactic.Common
public import Mathlib.Util.CompileInductive
deprecated_module (since... |
348 | lean_file_chunk | 81b8a902135105850a6c3630285abfb7002f567d229661f1589d23a67793102a | 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, Yury Kudryashov
-/
module
public import Mathlib.CategoryTheory.Category.Init
public import Mathlib.Tactic.Common
public import Mathlib.Util.CompileInductive
deprecated_mo... |
321 | lean_file_chunk | 6ed1cb9d693a9822d93e6097e05d0f1713de95f32fcdf5011777842e0c32ae58 | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.CategoryTheory.Category.Init
public import Mathlib.Data.Finset.Attr
public import Mathlib.Tactic.Common
public import Mathlib.Tactic.Finiteness.Attr
public import Mathlib.Tactic.SetLike
public import Mathlib.Util.CompileInductive
deprecated_module (since := "2025-11-28"... |
245 | lean_file_chunk | c437be22248f6bdf2e4ac9bfe947989391a92ed64251ddca392369f5b1798ecb | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.CategoryTheory.Category.Init
public import Mathlib.Tactic.Common
public import Mathlib.Tactic.Finiteness.Attr
public import Mathlib.Util.CompileInductive
deprecated_module (since := "2025-11-28") |
130 | lean_file_chunk | 8f81b4bd887c35cdefc0a790279a8b160a301254b3f54fbfb25fd05daa68a5ab | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.CategoryTheory.Subobject.Classifier.Defs
deprecated_module (since := "2026-03-03") |
9,609 | lean_file_chunk | c3ec77fa32052e70d71b6682dbbc35e70e8dc9e9671a30c2c97f0de6ab2927f2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Edward van de Meent. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Edward van de Meent
-/
module
public import Mathlib.CategoryTheory.Sites.Closed
public import Mathlib.CategoryTheory.Sites.Equivalence
public import Mathlib.CategoryTheory.Subobj... |
1,219 | lean_file_chunk | 80bf0523ff52b4998f2c17aedc5bd44d4ca9d96b8060d49d0a1de2c1957684e8 | 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.Filtered.Basic
public import Mathlib.CategoryTheory.WithTerminal.Basic
/-!
# Further lemmas on `WithTerminal`
These... |
10,327 | lean_file_chunk | 8eb9be6d7dd61c614e1ade3562f8f490fd4cc4c2e7917fd8da1a514056597cdd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Moisés Herradón Cueto. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moisés Herradón Cueto
-/
module
public import Mathlib.CategoryTheory.Comma.Over.Basic
public import Mathlib.CategoryTheory.WithTerminal.Basic
/-!
# Relations between `Cone`, `... |
23,998 | lean_file_chunk | 252d65eb52b632a4af8b0513057c06d113d69a44a216a916a1d0ae5353ad3b1f | 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: Joseph Tooby-Smith, Adam Topaz
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.IsTerminal
public import Mathlib.CategoryTheory.Limits.Shapes.Terminal
public import Mathlib.Ca... |
7,160 | lean_file_chunk | 1e2cc9c5062dd9083cf2935c87138ebbae533dbac483cfd3c566db966ca99333 | lean_source_file | pkg_mathlib_source_file_chunks | hom :=
{ app x := F.map (starInitial.to (.of x))
naturality x y f := by
dsimp
rw [Category.id_comp, ← F.map_comp]
congr 1 }
/-- A morphism of functors `WithInitial C ⥤ D` gives a morphism between the associated comma
objects. -/
@[simps!]
def mkCommaMorphism {F G : WithInitial C ⥤ D} ... |
2,297 | lean_file_chunk | 9c2c6b6c145c25ded22cfa96b4c5ec63847318943012d523ded7289477142702 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Moisés Herradón Cueto. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moisés Herradón Cueto
-/
module
public import Mathlib.CategoryTheory.FinCategory.Basic
public import Mathlib.CategoryTheory.WithTerminal.Basic
public import Mathlib.Data.Fintyp... |
10,434 | lean_file_chunk | 47d32ad442edd8ebc76be74ec41c39dafd71af825186097d3f6a5e1ca7fd5548 | 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.ExtremalEpi
public import Mathlib.CategoryTheory.MorphismProperty.Limits
public import Mathlib.CategoryTheory.Sites.Coherent.... |
1,342 | lean_file_chunk | ba5d721eda0d84e14dcd6dcf67776898d37a995119f68816f5ea8cc9559fb3ca | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
module
public import Mathlib.CategoryTheory.Filtered.CostructuredArrow
public import Mathlib.CategoryTheory.Functor.Flat
/-!
# Pulling back filteredness along r... |
23,937 | lean_file_chunk | a4c27e55cf9f3ef44734542d5c1da67a9f42e796a3ed1066696ce7a8063f0f84 | 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.Filtered.Connected
public import Mathlib.CategoryTheory.Limits.Final.Connected
public import Mathlib.CategoryTheory.Limits.... |
1,461 | lean_file_chunk | 9b318a3a5b74b6b76e30e864c16d6f66dc5ef5904eb6c61ff39248193abcbc1e | 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.Types.Colimits
public import Mathlib.CategoryTheory.Limits.Filtered
public import Mathlib.CategoryTheory.Limits.Yone... |
23,954 | lean_file_chunk | a056f21f5152b77d01a3f7eb2a9a80471a605c83adbeb038c746965b2f71d367 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits
public import Mathlib.Data.Fin.VecNotation
/-!
# Filtered categories
A category is f... |
17,043 | lean_file_chunk | 26b9c49128a59c9cc03ead9525ca779faac101caf0a33f236ac719dca1763988 | lean_source_file | pkg_mathlib_source_file_chunks | instance (priority := 100) isCofiltered_of_directed_ge_nonempty (α : Type u) [Preorder α]
[IsCodirectedOrder α] [Nonempty α] : IsCofiltered α where
-- Sanity checks
example (α : Type u) [SemilatticeInf α] [OrderBot α] : IsCofiltered α := by infer_instance
example (α : Type u) [SemilatticeInf α] [OrderTop α] : IsC... |
6,245 | lean_file_chunk | afae3b9d2ce5a130bf46d864b98a5196a090778f5dd1eb7af324376ffd75fa9f | 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.FinallySmall
public import Mathlib.CategoryTheory.Limits.Preserves.Filtered
/-!
# Finally small filtered categories
In thi... |
16,035 | lean_file_chunk | 483f6557b3105c762abe4ca793692b0d300f3c010747f07d4052a755da3ed41c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 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.EssentiallySmall
public import Mathlib.CategoryTheory.Filtered.Basic
public import Mathlib.Tactic.DepRewrite
/-!
# A funct... |
1,691 | lean_file_chunk | c336634014bc87dd2dbeb6047bbcf814769e78296b529f9178078266a1aad012 | 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.Filtered.Basic
public import Mathlib.CategoryTheory.Grothendieck
/-!
# Filteredness of Grothendieck construction
We show ... |
1,264 | lean_file_chunk | c70dcfb86f9a2446d402736077f3376fc63a2249a0ee4847057285b6722234b6 | 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.Filtered.Basic
public import Mathlib.CategoryTheory.IsConnected
/-!
# Filtered categories are connected
-/
public section... |
3,396 | lean_file_chunk | 7bdfc38a5dd1b4cb70d8860ca2d050806c54fba1198f3c7bc85a132130ec370d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
module
public import Mathlib.CategoryTheory.Filtered.OfColimitCommutesFiniteLimit
public import Mathlib.CategoryTheory.Functor.KanExtension.Adjunction
public imp... |
7,417 | lean_file_chunk | f7bc552bb8836e594e4ca9edae610ae774af55d13efd208d9a82022addfdd8e7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Whiskering
public import Mathlib.CategoryTheory.Functor.FullyFaithful
public import Mathlib.CategoryTheory.NatIso
/-!
# Disj... |
5,842 | lean_file_chunk | 7aa4ddc0f9d2902726f650f244da9b2cd5d84139eca1db96d3e4c01ef3eee694 | 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.ExtremalEpi
public import Mathlib.CategoryTheory.Generator.Basic
public import Mathlib.CategoryTheory.Limits.Presentation
/-!
# St... |
2,508 | lean_file_chunk | 62b752faacb1678c7fecf4ac9a4a2c1492de089aad360c3c8dafbcf74dcfc770 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.Algebra.Homology.Double
public import Mathlib.Algebra.Homology.HomologicalComplexLimits
public import Mathlib.CategoryTheory.Generator.Basic
/-!
... |
2,461 | lean_file_chunk | 849105b184313c31877a8cc922eddfd6aa72c59113fc7f102bd20c5fd06bfcef | 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.Abelian.Subobject
public import Mathlib.CategoryTheory.Limits.EssentiallySmall
public import Mathlib.CategoryTheory.Preaddi... |
3,182 | lean_file_chunk | 46931f99556095c028d5becc3e4570510bf43f8e8723ef0a92abd272c5c2e5a2 | 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.Generator.Basic
public import Mathlib.CategoryTheory.Limits.FunctorCategory.Basic
/-!
# Generators in the category of presheaves
... |
1,171 | lean_file_chunk | 26961d089d45513afbd22c7393ef5160418e543584aebcbca6d9e341cbe8e9a1 | 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.Generator.Basic
public import Mathlib.CategoryTheory.Limits.Indization.Category
public import Mathlib.CategoryTheory.Preadd... |
570 | lean_file_chunk | 0c06ff1cd4c8c4314f892189f6c3b184e6aec3bfa3cd749a019cf5b461c37d68 | 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.Basic
/-!
# Generator of Type
In this file, we show that `PUnit` is a separator of the category `Type u`.
-/
public s... |
3,432 | lean_file_chunk | ba1b028f048bc5c40a03d2ef264cca5ebb51e71b20ff4f6feda19f94b643232f | 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.Generator.Basic
public import Mathlib.CategoryTheory.Preadditive.Yoneda.Basic
/-!
# Separators in preadditive categories
... |
23,937 | lean_file_chunk | a3c11c2f6461c1238c67b90ebaad4445ae53d9a28e98d9c5d39c208e899323d8 | 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.EssentiallySmall
public import Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers
public import Mathlib.Categ... |
16,964 | lean_file_chunk | db4b9e6b143f004efb29db2a84482a0f3fad18dc3d898bd0847a23768d5af037 | lean_source_file | pkg_mathlib_source_file_chunks | theorem isCodetector_op_iff (G : C) : IsCodetector (op G) ↔ IsDetector G := by
rw [IsDetector, IsCodetector, ← isCodetecting_op_iff, op_singleton]
theorem isCodetector_unop_iff (G : Cᵒᵖ) : IsCodetector (unop G) ↔ IsDetector G := by
rw [IsDetector, IsCodetector, ← isCodetecting_unop_iff, unop_singleton]
theorem is... |
2,574 | lean_file_chunk | ee9a7a82027bb43fd3b7b627f9a53ecfdd9cb4b6c45060f98640c316adf286a8 | 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.Generator.Presheaf
public import Mathlib.CategoryTheory.Sites.Sheafification
public import Mathlib.CategoryTheory.Sites.Limits
/-!... |
2,122 | lean_file_chunk | e155214e8d362db6a5047544ee9abd90f3399923d4f615cd49d7983e09c51461 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
module
public import Mathlib.CategoryTheory.Sites.Pretopology
public import Mathlib.Data.Set.Finite.Lattice
/-! # The Finite Pretopology
In this file we define the finite pr... |
5,085 | lean_file_chunk | 8acebd1dfec70cbee01e18cfb875117902cad9c3e03da973345acfdecde61626 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.CategoryTheory.Limits.Final
public import Mathlib.CategoryTheory.Limits.VanKampen
public import Mathlib.CategoryTheory.Sites.Hyperco... |
5,300 | lean_file_chunk | 4888aada500aaf24ea2413c6bea637860fb3f12824dc85f119246055a0bf3830 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.CategoryTheory.Sites.LocallySurjective
/-!
# Locally fully faithful functors into sites
## Main results
- `CategoryTheory.Functor.IsLocally... |
3,271 | lean_file_chunk | 6ffc5654072c3a22e9127ac3060dd81f408bbdc26613e36b45c7717d5e35a48f | 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.Cartesian.FunctorCategory
public import Mathlib.CategoryTheory.Monoidal.Subcategory
public import Mathlib.Category... |
21,380 | lean_file_chunk | 1f79c739c69225487cfc0f285ae21b52029fc0397c6f9d69be139d74edb34877 | 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.Sites.Subsheaf
public import Mathlib.CategoryTheory.Sites.CompatibleSheafification
public import Mathlib.CategoryThe... |
12,385 | lean_file_chunk | 5642bf2d3a1a20674cc4bd18395fefda05d5b24d6ec564c7fa3347fb6033c52e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Ben Eltschig. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ben Eltschig
-/
module
public import Mathlib.CategoryTheory.Sites.ConstantSheaf
/-!
# Global sections of sheaves
In this file we define a global sections functor `Sheaf.Γ : Sheaf J A ... |
11,012 | lean_file_chunk | 6aadeff7bd5aa8dde3f63e89e1464dd63f5b2b9e0f8ed00c4ac98f89e695a308 | 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.Sites.SheafOfTypes
public import Mathlib.CategoryTheory.EffectiveEpi.Basic
/-!
# Effective epimorphic sieves
We define the not... |
4,924 | lean_file_chunk | 97b3bf3a8ff98d2a0a897622524d7c718017129bc68485a9956c236838e2ada0 | 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.Sites.Hypercover.Zero
public import Mathlib.CategoryTheory.Limits.Types.Pullbacks
/-!
# The jointly surjective preco... |
14,060 | lean_file_chunk | 356e7b8af307dc79b32716983130adabada8b132286e81439d1021edd92feb51 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
module
public import Mathlib.CategoryTheory.Sites.Limits
public import Mathlib.CategoryTheory.Limits.FilteredColimitCommutesFiniteLimit
public import Mathlib.CategoryTheory.... |
5,309 | lean_file_chunk | ad7ce035c0c254188b77dada0f2f29b9f3d7a2fa78cc8c78e3ca8828f5b011c5 | 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.Concrete
public import Mathlib.CategoryTheory.Sites.LocallyBijective
/-!
# Morphisms of sheaves factor as a local... |
7,679 | lean_file_chunk | 28f361f0931d01a6c42f23f84bda45aacf582323d939a453fd4a4421bd49e1ea | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.CategoryTheory.Functor.Flat
public import Mathlib.CategoryTheory.Sites.Continuous
public import Mathlib.Tactic.ApplyFun
/-!
# Cover-preserving... |
8,830 | lean_file_chunk | 5e1f85e7d47e3943364c598551685bf4a8320e4879bd6fce7905dfe3e358bab2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
public import Mathlib.CategoryTheory.Sites.Sheaf
public import Mathlib.CategoryTheory.Sites.Whiskering
/-!
# The canonical topology on a category
We define the ... |
12,134 | lean_file_chunk | 6eb5ed2c449b3f2c8f39d2ad35e22e013b8201ab0bf302497d6c3b41c2ed5872 | 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.Elementwise
public import Mathlib.CategoryTheory.Limits.FunctorCategory.EpiMono
public import Mathlib.Tactic.CategoryTheory.Ele... |
7,085 | lean_file_chunk | d7a66a21c8d17b965ea98a40c1aa3030b8dbcdacac2620ece4b49ea45edca0b8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Sites.LocallySurjective
public import Mathlib.CategoryTheory.Sites.Localization
/-!
# Locally bijective morphisms of presheaves
L... |
18,648 | lean_file_chunk | adf9eb1cab8d7dc159452d29a490ad13d23488a122423de6244c3cb25f215642 | 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.Sites.PrecoverageToGrothendieck
public import Mathlib.CategoryTheory.Sites.Sheaf
/-!
# Coverages
A coverage `K` on a category ... |
8,319 | lean_file_chunk | 36d7ffdfb53cae77c81a8179fd06b276732bc1d266bd5efc233f92e28ab257b2 | 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.Monoidal.Closed.FunctorCategory.Basic
public import Mathlib.CategoryTheory.Localization.Monoidal.Braided
public import Mathlib.Cate... |
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