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 |
|---|---|---|---|---|---|
2,176 | lean_file_chunk | 03bccb14ffe4c647985f90f74f8f6e09d95885008a6efa7aaec6ddfc4ad29837 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.CategoryTheory.Monoidal.Cartesian.CommMon_
public import Mathlib.CategoryTheory.Monoidal.Cartesian.Grp_
public import Mathlib.CategoryTheory... |
23,959 | lean_file_chunk | 3ebc445a9c56ca9e54298d4bd71b378e54b28fc3ae941f337082801d2534804a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Kim Morrison, Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Simon Hudon, Adam Topaz, Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts
public import Mathlib... |
16,172 | lean_file_chunk | 2019ced353d9a5947e08e33c50c3810436e6275fa0d502b9aab4f6b84e29354d | lean_source_file | pkg_mathlib_source_file_chunks | rw [IsIso.eq_comp_inv, Category.assoc, IsIso.inv_comp_eq, prodComparison_natural]
/-- If the product comparison morphism is an iso, its inverse is natural in the right argument. -/
@[reassoc]
theorem prodComparison_inv_natural_whiskerLeft (g : B ⟶ B') [IsIso (prodComparison F A B')] :
inv (prodComparison F A B) ≫ ... |
1,301 | lean_file_chunk | 3153e3ad1adeed7fee4ddfda656a9e024607eab82ea7bf469262344574c3d16e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.CategoryTheory.Monoidal.Cartesian.Mon_
/-!
# Yoneda embedding of `CommMon C`
-/
public section
assert_not_exists MonoidWithZero
open Categ... |
4,193 | lean_file_chunk | 6a3e85826cb7058afbc8648241654a232db8d35a5d27466265c697d77e048d6c | 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.Algebra.Category.MonCat.Shrink
public import Mathlib.Algebra.Category.Grp.Shrink
public import Mathlib.CategoryTheory.Monoidal.Carte... |
1,520 | lean_file_chunk | 0c407f3baeecb9d3a8a850c85db997d154de7f27c0875c94a8f8fed3a61594b4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour
-/
module
public import Mathlib.CategoryTheory.Limits.Preorder
public import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
/-!
# The preorder category of a meet-se... |
4,683 | lean_file_chunk | b70cacf26bd2dae449b8a27d73aef448b7f8a0a7c7383b0697d0b0527850a8db | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Nicolas Rolland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolas Rolland
-/
module
public import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
/-!
# Chosen finite products in `Cat`
This file proves that the Cartesian product of a pair o... |
2,262 | lean_file_chunk | af4076b095d44803b2e0c65970d68a9072e19552a05b437723e8a70cb3700b52 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Lean FRO LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
public import Mathlib.CategoryTheory.Monoidal.Comon_
/-!
# Comonoid objects in a Cartesian monoidal... |
17,193 | lean_file_chunk | 83d44a431080543d8a99adbe6789327e703cbba666dbcf2eb92ef88ed7c59d14 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Markus Himmel, Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Andrew Yang
-/
module
public import Mathlib.Algebra.Category.MonCat.Limits
public import Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms
public import Ma... |
6,596 | lean_file_chunk | 9d1545f9acfc51146cf63af613a2f376fa5c01c26c3197e70c29799ade59a5e9 | 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.FunctorCategory.Basic
public import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
public import Mathlib.CategoryTheory.Mon... |
8,958 | lean_file_chunk | ad4c64097eda207522dee9e5235470ef854d092a546f1881a140dfc50834424b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Monoidal.DayConvolution
/-!
# Day functors
In this file, given a monoidal category `C` and a monoidal category `V`,
we de... |
9,273 | lean_file_chunk | 4070c15dcc9905aa2aba0e05167dbc93186668356c9a074445770116512f6abd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Monoidal.DayConvolution
/-!
# Braidings for Day convolution
In this file, we show that if `C` is a braided monoidal categ... |
11,651 | lean_file_chunk | a0859da1dae24c3fbfbf8fbfbac42d14c8ec1b806c5a23762064be506f443bce | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Monoidal.DayConvolution
public import Mathlib.CategoryTheory.Monoidal.Closed.Basic
public import Mathlib.CategoryTheory.Lim... |
1,143 | lean_file_chunk | fc7ee46a66b016aa2ce6c2b5f0a446e1c2994e4e7167cb8864510e7e8d650781 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Vilim Lendvaj. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vilim Lendvaj
-/
module
public import Mathlib.CategoryTheory.Monoidal.Functor
public import Mathlib.CategoryTheory.Monoidal.Types.Basic
public import Mathlib.CategoryTheory.Types.Basic... |
1,357 | lean_file_chunk | 9546a95bcf8ba7836ee4af3c6de46151ddf3cffcdde39ca3804b90ab33841e94 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Michael Jendrusch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Monoidal.Types.Basic
public import Mathlib.CategoryTheory.Monoidal.CoherenceLemmas
/-!
# `(𝟙_ C ⟶ -... |
3,846 | lean_file_chunk | 4a80df62d4212ef76582eb6b93a42b3e484d72be230c7660c4d414529a43ed0b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Michael Jendrusch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
public import Mathlib.CategoryTheory.Monoidal.Functor
/-!
# The category of... |
7,945 | lean_file_chunk | f8f567138c99dbf05d9b091d1ea49be90ccd475d0521a02a3dbcf0104abb27ba | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Monoidal.ExternalProduct.Basic
public import Mathlib.CategoryTheory.Functor.KanExtension.Pointwise
public import Mathlib.Ca... |
4,015 | lean_file_chunk | 39301f5eef55695ed87fcffe7ff5e3d9b05f5f90d80d5835a80e7e160a3941d1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Monoidal.FunctorCategory
public import Mathlib.CategoryTheory.Functor.Currying
/-!
# External product of diagrams in a mon... |
3,243 | lean_file_chunk | 88e7aaf54b1a067b2959985656c35a4524fd322ae1d31cece4b5333868f7e041 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Monoidal.Opposite
public import Mathlib.CategoryTheory.Monoidal.Mon_
/-!
# Monoid objects internal to monoidal opposites
... |
12,063 | lean_file_chunk | 04cfeb4dfcf2601fa8d9b06273b8d8046955acb7ec786d891d6bd857a8550678 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.CategoryTheory.Monoidal.Free.Basic
public import Mathlib.CategoryTheory.Discrete.Basic
/-!
# The monoidal coherence theorem
In this file... |
15,742 | lean_file_chunk | a4868e5af43e6eb42a4c340020425cf43247b22e947e030903325cf193fe6a2c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.CategoryTheory.Monoidal.Functor
/-!
# The free monoidal category over a type
Given a type `C`, the free monoidal category over `C` has a... |
3,589 | lean_file_chunk | b1acd7c81393e9b43818864cf18582d4336efa7854bb41900207102971386263 | 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.Monoidal.Rigid.Basic
/-!
# Transport rigid structures over a monoidal equivalence.
-/
@[expose] public section
namespace ... |
23,994 | lean_file_chunk | da98edfc8dfc80f10d482cd369ca4a4c050b64a2be6137b2e429f51025cb0865 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 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.Tactic.CategoryTheory.Monoidal.Basic
public import Mathlib.CategoryTheory.Monoidal.Closed.Basic
public import Mathlib.Tactic.ApplyFu... |
860 | lean_file_chunk | a13a17373c394195faa4d38085a1dafbee47bf8cbc7ef117939b26c74a1c86ae | lean_source_file | pkg_mathlib_source_file_chunks | `CategoryTheory.Monoidal.leftRigidFunctorCategory`. Moreover, in concrete applications there is
often a more useful definition of the internal hom object than `ᘁY ⊗ X`, in which case the monoidal
closed structure shouldn't come the rigid structure (e.g. in the category `FinVect k`, it is more
convenient to define the i... |
5,756 | lean_file_chunk | 9634ae9e7510074d0f89c3e229fddcdc683e8b88db74811501d1b9b86ac2dcee | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Gareth Ma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gareth Ma
-/
module
public import Mathlib.CategoryTheory.Monoidal.Rigid.Basic
public import Mathlib.CategoryTheory.Monoidal.Braided.Basic
/-!
# Deriving `RigidCategory` instance for braid... |
1,663 | lean_file_chunk | 00db714b2e42d7625478f7334f262277b5fcf085aed970a832cfbf7726cf0773 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Monoidal.Rigid.Basic
public import Mathlib.CategoryTheory.Monoidal.Opposite
/-!
# Dual Functors for Rigid Categories
This f... |
2,620 | lean_file_chunk | a50319eaeec3b6bedbcd84664250060e7bf4b81c7b683ad7087201f26a40f696 | 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.Monoidal.Rigid.Basic
public import Mathlib.CategoryTheory.Monoidal.FunctorCategory
/-!
# Functors from a groupoid into a rig... |
9,380 | lean_file_chunk | 9cfc53a49e129fb4444afa0d31082f967842bf37415d0a0084f8d95f8f1da2e4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic
public import Mathlib.Algebra.Category.AlgCat.Basic
public import Mathlib.CategoryTheory.Monoidal.... |
4,136 | lean_file_chunk | 21582554d44d6234e260d0183a790128b0068fa1db232c50a226f44ac8589075 | 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.Monoidal.Internal.FunctorCategory
public import Mathlib.CategoryTheory.Monoidal.Limits.Basic
public import Math... |
9,850 | lean_file_chunk | 2e3da9b31b9570cc224f649285a37ff1a8087d24cb46f08139469814a7cfa0a3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Monoidal.CommMon_
public import Mathlib.CategoryTheory.Monoidal.Comon_
public import Mathlib.CategoryTheory.Monoidal.FunctorC... |
2,031 | lean_file_chunk | e2db51f42969a30f500dd96e32402ac11a3647b96a84aed66d24275181e6fc36 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Jack McKoen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jack McKoen
-/
module
public import Mathlib.CategoryTheory.Limits.HasLimits
public import Mathlib.CategoryTheory.Monoidal.Category
/-!
# Compatibility lemmas for limits and colimits in ... |
2,387 | lean_file_chunk | fcc768a303436f6580356a158d907f74932ed34a9572e3be69e10a50c07a4294 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Limits.Preserves.BifunctorCokernel
public import Mathlib.CategoryTheory.Monoidal.Preadditive
/-!
# Tensor products of cokernels
L... |
2,911 | lean_file_chunk | 059d38280ed81af2335f7f3c8ea4f949e2b6764a2816e2e2009499d7dd0417a2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Monoidal.Braided.Basic
public import Mathlib.CategoryTheory.Limits.FunctorCategory.Basic
/-!
# Miscellany about preservati... |
3,625 | lean_file_chunk | 62825bc9214fb57d31acd26e03a123f5f495128064b7bbf75438cb6a5e4bf091 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Monoidal.FunctorCategory
public import Mathlib.CategoryTheory.Limits.HasLimits
/-!
# `lim : (J ⥤ C) ⥤ C` is lax monoidal whe... |
2,751 | lean_file_chunk | 16db2e42312b992e29b4d6d3df54bf4e1c1b7995fcfce6b9d2a76b693757a403 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Limits.Sifted
/-!
# Tensor product of colimits
In this file, we apply the `PreservesColimit₂` API to the bifunctor
`curriedTensor... |
2,187 | lean_file_chunk | 8d7096b4cb1e85c86f66469e96cb7879b01fe16034d292e6ee8af1b84e36c240 | 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.Functor.FunctorHom
public import Mathlib.CategoryTheory.Monoidal.Closed.Basic
/-!
# Functors to Type are closed.
Show that `C... |
723 | lean_file_chunk | 451b698b69c08e2e8f8f66864ad37ddad5636e7e1e5c99d5023a37421d26d282 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Monoidal.Closed.Basic
public import Mathlib.CategoryTheory.Monoidal.Transport
/-!
# Transporting a closed monoidal ... |
2,692 | lean_file_chunk | 6b6c78321c427bfb619c6984cf6a2c4877b1c9c9a7afaab13db3b09df0b06aac | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Daniel Carranza. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Carranza, Joël Riou
-/
module
public import Mathlib.CategoryTheory.Enriched.Ordinary.Basic
public import Mathlib.CategoryTheory.Monoidal.Closed.Basic
/-!
# A closed monoidal ... |
20,650 | lean_file_chunk | 70c83d60195b418586e2ae4b427c4fda4910e8cd23d7c0562f044fba2e61336d | 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, Daniel Carranza, Joël Riou
-/
module
public import Mathlib.CategoryTheory.Monoidal.Functor
public import Mathlib.CategoryTheory.Monoidal.CoherenceLemmas
publ... |
9,967 | lean_file_chunk | a8c49e421779d784b13f94ede8493bd0d0dc84bca65a1b6d672e44e6e16b29ae | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Bhavik Mehta, Edward Ayers, Thomas Read. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Edward Ayers, Thomas Read
-/
module
public import Mathlib.CategoryTheory.Monoidal.Closed.Basic
public import Mathlib.CategoryTheory.Monoidal.Car... |
16,224 | lean_file_chunk | 17481aaf169919086c4a5b39804e248ec06569d330ea2b32819bf3a2a3393238 | 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.Limits.Preserves.Shapes.BinaryProducts
public import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal
public import Ma... |
766 | lean_file_chunk | 972b34c1a236614cf9510a0b4bc81e8978283619989b46c1b0ad0dc1f404df54 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Jack McKoen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jack McKoen
-/
module
public import Mathlib.CategoryTheory.Monoidal.Braided.Basic
public import Mathlib.CategoryTheory.Monoidal.Closed.Basic
/-!
# Closed braided monoidal categories
In... |
8,439 | lean_file_chunk | 0b38249d4895a4b8703543b61a6177c183a0654e1577ab88ee0d4664503dbd69 | 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.Preserves.Shapes.BinaryProducts
public import Mathlib.CategoryTheory.Adjunction.FullyFaithful
public import Mathlib.Ca... |
3,386 | lean_file_chunk | 05a2454cc47171de09801eaa912b83feefc6b576302ed7ce11684505d61a7981 | 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.Monoidal.Closed.Cartesian
public import Mathlib.CategoryTheory.Limits.Presheaf
public import Mathlib.CategoryTheory.Monoidal.... |
2,241 | lean_file_chunk | 9a6628f04b147a2dccf6e5baa294f517a2ec611fa1de0ad6dfadabc8af985ed4 | 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.Monoidal.Closed.Cartesian
public import Mathlib.CategoryTheory.PUnit
public import Mathlib.CategoryTheory.Limits.Shapes.ZeroO... |
12,914 | lean_file_chunk | b59e9c064e25051f5d796d0430446dc0b16eee4fb94fc5a89e44576be8785908 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Monoidal.Action.Basic
/-! # Functors that are linear with respect to an action
Given a monoidal category `C` acting on th... |
23,974 | lean_file_chunk | 5c193f83d0ea45b2c94eda5c8a9058ba53777e4ab8a2063409ef8f1df903a46b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Monoidal.Category
public import Mathlib.CategoryTheory.Functor.Trifunctor
/-!
# Actions from a monoidal category on a cat... |
2,147 | lean_file_chunk | 842b68e820e1c549efda9e4d8d056afbc2f3e97228aaa46a15ea4f2e89bfeeb1 | lean_source_file | pkg_mathlib_source_file_chunks | inv f ⊵ᵣ z ≫ f ⊵ᵣ z = 𝟙 (y ⊙ᵣ z) := by
rw [← comp_actionHomLeft, IsIso.inv_hom_id, id_actionHomLeft]
instance isIso_actionHomLeft {x y : D} (f : x ⟶ y) [IsIso f] (z : C) :
IsIso (f ⊵ᵣ z) :=
⟨inv f ⊵ᵣ z, by simp⟩
instance isIso_actionHomRight (x : D) {y z : C} (f : y ⟶ z) [IsIso f] :
IsIso (x ⊴ᵣ f) :=
⟨... |
8,212 | lean_file_chunk | ffa56a751ca454386a0ee13619b1b184961cca7456afcae5ea4c08367c4a354e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Monoidal.Action.Basic
public import Mathlib.CategoryTheory.Monoidal.End
public import Mathlib.CategoryTheory.Monoidal.Oppos... |
16,026 | lean_file_chunk | 91a13146720671d40808235f27ee44cc3036daa1be43d792f7325261f666c5b9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Monoidal.Action.Basic
public import Mathlib.CategoryTheory.Monoidal.Opposite
/-!
# Actions from the monoidal opposite of ... |
3,038 | lean_file_chunk | b9ce9c90f6da7ddadf86e7e970bd09ada22f48fa6b96ab0a2b31fcb0e0e0497f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Monoidal.Braided.Basic
public import Mathlib.CategoryTheory.Monoidal.Transport
/-!
# Transport a symmetric monoidal... |
1,363 | lean_file_chunk | cf8b7a7513414e760fef7045f7796abc75711730123e815bd8fbbb05333518e7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Lean FRO LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Monoidal.Braided.Basic
public import Mathlib.CategoryTheory.Monoidal.Opposite
/-!
# If `C` is braided, so is `Cᵒᵖ`.
Todo: w... |
11,454 | lean_file_chunk | 45d6de2c7953dd0dca452726fa4e3fc23e7b457067f65bf222ca4c0e0b9147fc | 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.Adjunction.Restrict
public import Mathlib.CategoryTheory.Monoidal.Closed.Basic
public import Mathlib.CategoryTheory.M... |
23,942 | lean_file_chunk | 88223d379b453329317b2ce2a344caae62d7e4685644a9e3915f0a4a8b6ecb20 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Monoidal.Discrete
public import Mathlib.CategoryTheory.Monoidal.NaturalTransformation
public import Mathlib.CategoryTheory.Mo... |
10,858 | lean_file_chunk | 88d2e901ccba93a062cf6d19f762dbe61e70b10b5bfcabcbc7dbe249ba2b44a8 | lean_source_file | pkg_mathlib_source_file_chunks | rw [tensorHom_comp_tensorHom, tensorHom_comp_tensorHom, comp_id f₁, ← id_comp f₁, comp_id g₂,
← id_comp g₂, braiding_naturality, ← tensorHom_comp_tensorHom, ← tensorHom_comp_tensorHom]
slice_lhs 4 5 =>
rw [tensorHom_comp_tensorHom, comp_id f₁, ← id_comp f₁, associator_naturality,
← tensorHom_comp_tens... |
9,230 | lean_file_chunk | 21a1709fbc6e48567aab266c9959b020e9fc9ac9b3ae8eb94e3a45956d892b2d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Monoidal.Braided.Basic
public import Mathlib.CategoryTheory.Functor.CurryingThree
/-!
# Constructing braided catego... |
2,415 | lean_file_chunk | fe8bd4dd6e383eace8814da7a4160ceed230cdc7150093268653c4c547c40795 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.CategoryTheory.Monoidal.Internal.Types.Basic
public import Mathlib.CategoryTheory.Monoidal.Grp_
public import Mathlib.Algebra.Category.Grp... |
3,342 | lean_file_chunk | df1d841992646b501592291cca0db0afdf48551b4a4d795f0b7f75cc5cda74ea | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.CategoryTheory.Monoidal.Internal.Types.Grp_
public import Mathlib.CategoryTheory.Monoidal.CommGrp_
/-!
# `CommGrp (Type u) ≌ CommGrpCat.{... |
5,075 | lean_file_chunk | a4265922484df3761feec590f9b472437d27c79d5fe73e641f694f558ee1dca5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Algebra.Category.MonCat.Basic
public import Mathlib.CategoryTheory.Monoidal.CommMon_
public import Mathlib.CategoryTheory.Monoidal.Types.Bas... |
5,886 | lean_file_chunk | 6694af6ea86797f804788a008337da0c305036cd76a988e9cdbce7bc39711d4f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Jack McKoen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jack McKoen
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs
public import Mathlib.CategoryTheory.Monoidal.Category
/-!
# Pullbacks and pushouts in ... |
3,236 | lean_file_chunk | a890ef5b337777340e1b511589015f9214257bb38a11c88bcdc5bba802535ed8 | 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.Adjunction.Lifting.Right
public import Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Groupoid
public import ... |
3,030 | lean_file_chunk | 1db3b3b0f4fbec1a5bf39c8ee2f14d37727edc5283bbe071d806240c6c48d4e7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Antoine Labelle. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle
-/
module
public import Mathlib.CategoryTheory.Monoidal.Closed.Basic
public import Mathlib.CategoryTheory.Functor.Currying
public import Mathlib.CategoryTheory.Monoid... |
5,767 | lean_file_chunk | 774b3449690fdac449162657217f8f9a35a15337357c830caa8d79fc6f3b5346 | 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.Enrichment
public import Mathlib.CategoryTheory.Enriched.FunctorCategory
/-!
# Functor categories are monoidal clo... |
15,439 | lean_file_chunk | 98cfc4c04e85f32e6ea5a8f1c2d674050f144f563895750074d8bbbd64ea1cee | 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.Enriched.Basic
public import Mathlib.CategoryTheory.Monoidal.Types.Coyoneda
/-!
# Enriched ordinary categories
If `V` is a monoid... |
1,387 | lean_file_chunk | 119102d2214e51afb546bd374cbeebada4cbdffac77415a5eb6a5ffa01828d3a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jon Eugster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Jon Eugster, Emily Riehl
-/
module
public import Mathlib.CategoryTheory.Enriched.Limits.HasConicalLimits
/-!
# Existence of conical products
-/
@[expose] public secti... |
1,280 | lean_file_chunk | 22d45a31a938b7e096c54342e1104a4a851434afe8806ba842a0279e0fe55af9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jon Eugster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Jon Eugster, Emily Riehl
-/
module
public import Mathlib.CategoryTheory.Enriched.Limits.HasConicalLimits
/-!
# Existence of conical pullbacks
-/
@[expose] public sect... |
994 | lean_file_chunk | f02a43c155ceea263d9273fc490b4f91745c4edb329eebf573e4a871381cadba | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jon Eugster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Jon Eugster, Emily Riehl
-/
module
public import Mathlib.CategoryTheory.Enriched.Limits.HasConicalProducts
/-!
# Existence of conical terminal objects
-/
@[expose] pu... |
5,359 | lean_file_chunk | c8e9272405ac60925208aa2be6de232c9c8f061aeaf93b27019777f5c5620e90 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jon Eugster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jon Eugster, Dagur Asgeirsson, Emily Riehl
-/
module
public import Mathlib.CategoryTheory.Enriched.Ordinary.Basic
public import Mathlib.CategoryTheory.Limits.Final
/-!
# Existence of co... |
8,476 | lean_file_chunk | 32a0ead6117e925fda258423d2154f4c3f88b32082efa54dc4e71e71b0c5c51a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
module
public import Mathlib.CategoryTheory.Bicategory.Functor.Prelax
public import Mathlib.Tactic.CategoryTheory.ToApp
/-!
# Oplax functors
An oplax functor `F` between... |
6,092 | lean_file_chunk | abcba0b144ca52c21ab02d80d865543f8720dca4ecc8801ca1c0eeab3ab431b5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne
-/
module
public import Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary
/-!
# Strict pseudofunctors
In this file we introduce the notion of strict pseudofunctors,... |
13,933 | lean_file_chunk | d82a9e858deef99357b9e4b90c4a2ff12e8df92c37f43c63c5eb200b5b5e14d7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno, Calle Sönne
-/
module
public import Mathlib.CategoryTheory.Bicategory.Functor.Oplax
public import Mathlib.CategoryTheory.Bicategory.Functor.Lax
public import Mathlib.Tactic.... |
9,122 | lean_file_chunk | 5c3a6737f758ae567e0d42ef9e1558e3584a50d0be1a81f1bbf2c43c67461562 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne
-/
module
public import Mathlib.CategoryTheory.Bicategory.Functor.Prelax
public import Mathlib.Tactic.CategoryTheory.Slice
public import Mathlib.Tactic.CategoryTheory.ToApp
... |
6,856 | lean_file_chunk | 7e750c3ab2b3ad87113ce3875bf2f2fdee464549c219ed1b96a3e430de5d0db7 | 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: Yuma Mizuno, Calle Sönne
-/
module
public import Mathlib.CategoryTheory.Bicategory.Basic
public import Mathlib.CategoryTheory.EqToHom
/-!
# Prelax functors
This file defines lax prefu... |
2,556 | lean_file_chunk | 9470fbb10364bf0733df96a2c4defcb3d12340276ca31826fbfc2af9ce982462 | 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, Christian Merten
-/
module
public import Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor
/-!
# Pseudofunctors to Cat
In this file, we state naturality properties of `m... |
7,370 | lean_file_chunk | 0f593e8202c59faaf71238752bb6fca7df8452c37c0502d58c2da3151234e09c | 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.Bicategory.Functor.Pseudofunctor
public import Mathlib.CategoryTheory.Bicategory.LocallyDiscrete
/-!
# Pseudofunctors from locally... |
12,311 | lean_file_chunk | f2981c20e4f8b8cf05ffcd69f56d2db88e51c369042c70468cd658be991314e3 | 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.Bicategory.Functor.Pseudofunctor
/-!
# Strictly unitary lax functors and pseudofunctors
In this file, we define strictly ... |
18,989 | lean_file_chunk | d82b675ae4fbecef60e043cc841ba66dc391b0db8d4b244fb0197068e8a1629a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno, Calle Sönne
-/
module
public import Mathlib.CategoryTheory.Bicategory.Functor.Oplax
public import Mathlib.Tactic.CategoryTheory.Bicategory.Basic
/-!
# Transformations betwe... |
16,768 | lean_file_chunk | 57b5a1c994cf3d73a4c07906ef819741ba02aaaad8eceae0b10055a195605580 | 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: Yuma Mizuno, Calle Sönne, Robin Carlier
-/
module
public import Mathlib.CategoryTheory.Bicategory.Functor.Lax
public import Mathlib.Tactic.CategoryTheory.Bicategory.Basic
/-!
# Transf... |
10,135 | lean_file_chunk | 85921d766148cf046389ff0694d2eb2bc3e9061c2a4a46cfe9ed78939298fb74 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne
-/
module
public import Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor
public import Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Oplax
/-!
# Strong tra... |
12,822 | lean_file_chunk | c02a1557fc7f670bc391200f200cb046739e03e90e483e738769b55f27ac4fa5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno, Calle Sönne
-/
module
public import Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Oplax
/-!
# Modifications between transformations of oplax functors
In this fil... |
6,953 | lean_file_chunk | 0e1d387a53f0efb98044557590d61fb8e492b70328c3121fdc10f28451766fa6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
module
public import Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Lax
/-!
# Modifications between transformations of lax functors
In this file we define modif... |
5,613 | lean_file_chunk | b464a17ac063ce4af187769d3b49314d37c1c13debc16499a1b34d47e0b156f7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne
-/
module
public import Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Pseudo
public import Mathlib.CategoryTheory.Bicategory.Modification.Oplax
/-!
# Modifications... |
8,624 | lean_file_chunk | 1c8b3b9f01058484797d6b96f4971523501dda06107837d44858028e8074cbd4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
module
public import Mathlib.CategoryTheory.Bicategory.Extension
/-!
# Kan extensions and Kan lifts in bicategories
The left Kan extension of a 1-morphism `g : a ⟶ c` al... |
10,861 | lean_file_chunk | 1168f7fc9887dc49c0e3de8bbd5c6975921f0d402ff314fce4af61566aa6e40f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
module
public import Mathlib.CategoryTheory.Bicategory.Kan.HasKan
public import Mathlib.CategoryTheory.Bicategory.Adjunction.Basic
public import Mathlib.Tactic.TFAE
/-!
#... |
12,125 | lean_file_chunk | 0e49d78ede3f860850dc49afa97d46c8d52f1fa49d7bff76dbb3d29704dc6504 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Terminal
public import Mathlib.CategoryTheory.Bicategory.Kan.IsKan
/-!
# Existence of Kan extensions and Kan lif... |
10,417 | lean_file_chunk | 9222ef53377cae56f12499dd6667ceb5233cf52935f757bf0b53f5bd7edc867c | 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, Christian Merten
-/
module
public import Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor
public import Mathlib.CategoryTheory.CommSq
/-!
# Pseudofunctors from strict bi... |
2,802 | lean_file_chunk | 9f1bc4ff63ab2217e3e478d153fa65b4d1c0a6a03a465107796442cd47da31e2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
module
public import Mathlib.CategoryTheory.EqToHom
public import Mathlib.CategoryTheory.Bicategory.Basic
/-!
# Strict bicategories
A bicategory is called `Strict` if th... |
5,625 | lean_file_chunk | 32430e994618acf37beb348104f147da948c8cdae2eb19177b51c74b0d677ee8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
module
public import Mathlib.CategoryTheory.Bicategory.LocallyDiscrete
public import Mathlib.CategoryTheory.Bicategory.FunctorBicategory.Oplax
public import Mathlib.Catego... |
11,780 | lean_file_chunk | 527da7196c058fb4a5cb16086e41056a596258a4e1866de4da2c09bb439be1f1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
module
public import Mathlib.Tactic.CategoryTheory.Bicategory.Basic
public import Mathlib.Tactic.CategoryTheory.BicategoricalComp
/-!
# Adjunctions in bicategories
For 1... |
23,996 | lean_file_chunk | 26f844fcc29049b066209d2095700822d06a4cf34ed7586f10b90b37c8d53699 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno, Joël Riou
-/
module
public import Mathlib.CategoryTheory.Bicategory.Adjunction.Basic
public import Mathlib.CategoryTheory.HomCongr
/-!
# Mates in bicategories
This file es... |
4,428 | lean_file_chunk | c91b5d317f02a01b4897c16a27cd9943ad0fc5415a436716e164f72e03c65348 | lean_source_file | pkg_mathlib_source_file_chunks | end ConjugateIsomorphism
section IteratedMateEquiv
variable {a b c d : B}
variable {f₁ : a ⟶ c} {u₁ : c ⟶ a} {f₂ : b ⟶ d} {u₂ : d ⟶ b}
variable {l₁ : a ⟶ b} {r₁ : b ⟶ a} {l₂ : c ⟶ d} {r₂ : d ⟶ c}
variable (adj₁ : l₁ ⊣ r₁) (adj₂ : l₂ ⊣ r₂) (adj₃ : f₁ ⊣ u₁) (adj₄ : f₂ ⊣ u₂)
/-- When all four morphisms in a square are l... |
4,432 | lean_file_chunk | a3be8f071ca65b26113eb40bc8f84b15ccd61feee52a9577c0464435ed7709b1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Adjunction.Mates
public import Mathlib.CategoryTheory.Bicategory.Adjunction.Adj
/-!
# Adjunctions in `Cat`
We show that adjunctio... |
6,612 | lean_file_chunk | 8a25a0378b49158515009527932b52cd90387e2e89bac219d026eafb6dc7bdd2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Bicategory.Adjunction.Mate
public import Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor
/-!
# The bicategory of adjunctio... |
5,387 | lean_file_chunk | a8c8365d6f1c4f537315f79244d83f009ed5931d270abc3a491c67cdcfda3d5c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
module
public import Mathlib.CategoryTheory.Bicategory.Modification.Oplax
/-!
# Bicategories of oplax functors
Given bicategories `B` and `C`, we give bicategory structu... |
6,193 | lean_file_chunk | e0b74f12218c19a3429bb164d83b6ed1cb890dc2fbfb49031bf3001f0a633dd3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
module
public import Mathlib.CategoryTheory.Bicategory.Modification.Lax
/-!
# Bicategories of lax functors
Given bicategories `B` and `C`, we give bicategory structures ... |
3,358 | lean_file_chunk | e80c512cb37d5ec010dcf69278e1c3c2e300f985c3dbf0025c0696278435c33e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne
-/
module
public import Mathlib.CategoryTheory.Bicategory.Modification.Pseudo
/-!
# The bicategory of pseudofunctors
Given bicategories `B` and `C`, we define a bicategory ... |
5,379 | lean_file_chunk | d9a181b357da2d8b287e7aba772ea479e1f19e4f0da3d925b47f37be96e158cf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Pseudo
/-!
# Properties of objects in target categories of a pseudofunctor to `Cat`
Given `F : P... |
8,109 | lean_file_chunk | 4e1ff538e954792bbab9d23958b1d4ebe5a3931f9c452dfca467ebc50fde3e18 | 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.Triangulated.Adjunction
public import Mathlib.CategoryTheory.Triangulated.Opposite.Basic
/-!
# The triangulated equivalence `Cᵒᵖᵒᵖ... |
4,686 | lean_file_chunk | 3657a8d29574f66e5e44340642bfcaae939b33c06036e957134dd9842baa601e | 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.Triangulated.Basic
public import Mathlib.CategoryTheory.Triangulated.Opposite.Basic
/-!
# Triangles in the opposite category of a ... |
2,384 | lean_file_chunk | 9a1001cf6653ad43d5c5844b61adca71e39da6722c403df9b2d038c7e803ae67 | 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, Justus Springer
-/
module
public import Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated
/-!
# The opposite of a triangulated category is triangulated
The pretrian... |
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