path stringlengths 11 71 | content stringlengths 75 124k |
|---|---|
CategoryTheory\Adjunction\Limits.lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Johan Commelin
-/
import Mathlib.CategoryTheory.Adjunction.Basic
import Mathlib.CategoryTheory.Limits.Creates
/-!
# Adjunctions and limits
A left adjoint preserves colimits... |
CategoryTheory\Adjunction\Mates.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Emily Riehl
-/
import Mathlib.CategoryTheory.Adjunction.Basic
import Mathlib.CategoryTheory.HomCongr
import Mathlib.Tactic.ApplyFun
/-!
# Mate of natural transformations
... |
CategoryTheory\Adjunction\Opposites.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Thomas Read, Andrew Yang
-/
import Mathlib.CategoryTheory.Adjunction.Basic
import Mathlib.CategoryTheory.Yoneda
import Mathlib.CategoryTheory.Opposites
/-!
# Opposite adju... |
CategoryTheory\Adjunction\Over.lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Andrew Yang
-/
import Mathlib.CategoryTheory.Adjunction.Mates
import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Limits.Shapes.Pullba... |
CategoryTheory\Adjunction\Reflective.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.CategoryTheory.Adjunction.FullyFaithful
import Mathlib.CategoryTheory.Functor.ReflectsIso
import Mathlib.CategoryTheory.HomCongr
/-!
# Reflective functors... |
CategoryTheory\Adjunction\Restrict.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.CategoryTheory.Adjunction.Basic
import Mathlib.CategoryTheory.HomCongr
/-!
# Restricting adjunctions
`Adjunction.restrictFullyFaithful` shows that an... |
CategoryTheory\Adjunction\Unique.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Thomas Read, Andrew Yang, Dagur Asgeirsson, Joël Riou
-/
import Mathlib.CategoryTheory.Adjunction.Basic
/-!
# Uniqueness of adjoints
This file shows that adjoints are uni... |
CategoryTheory\Adjunction\Whiskering.lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import Mathlib.CategoryTheory.Whiskering
import Mathlib.CategoryTheory.Adjunction.Basic
/-!
Given categories `C D E`, functors `F : D ⥤ E` and `G : E ⥤ D` with an adjunctio... |
CategoryTheory\Bicategory\Adjunction.lean | /-
Copyright (c) 2023 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
import Mathlib.Tactic.CategoryTheory.Coherence
/-!
# Adjunctions in bicategories
For 1-morphisms `f : a ⟶ b` and `g : b ⟶ a` in a bicategory, an adjunction between `f` an... |
CategoryTheory\Bicategory\Basic.lean | /-
Copyright (c) 2021 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
import Mathlib.CategoryTheory.NatIso
/-!
# Bicategories
In this file we define typeclass for bicategories.
A bicategory `B` consists of
* objects `a : B`,
* 1-morphisms ... |
CategoryTheory\Bicategory\Coherence.lean | /-
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno, Junyan Xu
-/
import Mathlib.CategoryTheory.PathCategory
import Mathlib.CategoryTheory.Functor.FullyFaithful
import Mathlib.CategoryTheory.Bicategory.Free
import Mathlib.Categ... |
CategoryTheory\Bicategory\End.lean | /-
Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.CategoryTheory.Bicategory.Basic
import Mathlib.CategoryTheory.Monoidal.Category
/-!
# Endomorphisms of an object in a bicategory, as a monoidal catego... |
CategoryTheory\Bicategory\Extension.lean | /-
Copyright (c) 2023 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
import Mathlib.CategoryTheory.Bicategory.Basic
import Mathlib.CategoryTheory.Comma.StructuredArrow
/-!
# Extensions and lifts in bicategories
We introduce the concept of ... |
CategoryTheory\Bicategory\Free.lean | /-
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
import Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor
/-!
# Free bicategories
We define the free bicategory over a quiver. In this bicategory, the 1-morphisms ar... |
CategoryTheory\Bicategory\FunctorBicategory.lean | /-
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
import Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Oplax
/-!
# The bicategory of oplax functors between two bicategories
Given bicategories `B` and `C`, we gi... |
CategoryTheory\Bicategory\LocallyDiscrete.lean | /-
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
-/
import Mathlib.CategoryTheory.DiscreteCategory
import Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor
import Mathlib.CategoryTheory.Bicategory.Strict
... |
CategoryTheory\Bicategory\SingleObj.lean | /-
Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.CategoryTheory.Bicategory.End
import Mathlib.CategoryTheory.Monoidal.Functor
/-!
# Promoting a monoidal category to a single object bicategory.
A mon... |
CategoryTheory\Bicategory\Strict.lean | /-
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
import Mathlib.CategoryTheory.EqToHom
import Mathlib.CategoryTheory.Bicategory.Basic
/-!
# Strict bicategories
A bicategory is called `Strict` if the left unitors, the ri... |
CategoryTheory\Bicategory\Functor\Lax.lean | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne
-/
import Mathlib.CategoryTheory.Bicategory.Functor.Prelax
import Mathlib.Tactic.CategoryTheory.Slice
/-!
# Lax functors
A lax functor `F` between bicategories `B` and `C` ... |
CategoryTheory\Bicategory\Functor\Oplax.lean | /-
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
import Mathlib.CategoryTheory.Bicategory.Functor.Prelax
/-!
# Oplax functors
An oplax functor `F` between bicategories `B` and `C` consists of
* a function between object... |
CategoryTheory\Bicategory\Functor\Prelax.lean | /-
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
-/
import Mathlib.CategoryTheory.Bicategory.Basic
/-!
# Prelax functors
This file defines lax prefunctors and prelax functors between bicategories. The point ... |
CategoryTheory\Bicategory\Functor\Pseudofunctor.lean | /-
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
-/
import Mathlib.CategoryTheory.Bicategory.Functor.Oplax
import Mathlib.CategoryTheory.Bicategory.Functor.Lax
/-!
# Pseudofunctors
A pseudofunctor is an oplax ... |
CategoryTheory\Bicategory\Kan\Adjunction.lean | /-
Copyright (c) 2024 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
import Mathlib.CategoryTheory.Bicategory.Kan.HasKan
import Mathlib.CategoryTheory.Bicategory.Adjunction
import Mathlib.Tactic.TFAE
/-!
# Adjunctions as Kan extensions
We ... |
CategoryTheory\Bicategory\Kan\HasKan.lean | /-
Copyright (c) 2024 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
import Mathlib.CategoryTheory.Bicategory.Kan.IsKan
/-!
# Existence of Kan extensions and Kan lifts in bicategories
We provide the propositional typeclass `HasLeftKanExten... |
CategoryTheory\Bicategory\Kan\IsKan.lean | /-
Copyright (c) 2023 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
import Mathlib.CategoryTheory.Bicategory.Extension
/-!
# Kan extensions and Kan lifts in bicategories
The left Kan extension of a 1-morphism `g : a ⟶ c` along a 1-morphis... |
CategoryTheory\Bicategory\NaturalTransformation\Oplax.lean | /-
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
import Mathlib.CategoryTheory.Bicategory.Functor.Oplax
/-!
# Oplax natural transformations
Just as there are natural transformations between functors, there are oplax nat... |
CategoryTheory\Bicategory\NaturalTransformation\Strong.lean | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne
-/
import Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor
import Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Oplax
/-!
# Strong natural transformations
... |
CategoryTheory\Category\Basic.lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison, Johannes Hölzl, Reid Barton
-/
import Mathlib.CategoryTheory.Category.Init
import Mathlib.Combinatorics.Quiver.Basic
import Mathlib.Tactic.PPWithUniv
im... |
CategoryTheory\Category\Bipointed.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.CategoryTheory.Category.Pointed
/-!
# The category of bipointed types
This defines `Bipointed`, the category of bipointed types.
## TODO
Monoidal struc... |
CategoryTheory\Category\Cat.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.CategoryTheory.ConcreteCategory.Bundled
import Mathlib.CategoryTheory.DiscreteCategory
import Mathlib.CategoryTheory.Types
import Mathlib.CategoryThe... |
CategoryTheory\Category\Factorisation.lean | /-
Copyright (c) 2023 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
import Mathlib.CategoryTheory.Category.Basic
import Mathlib.CategoryTheory.Comma.Arrow
import Mathlib.CategoryTheory.Limits.Shapes.Terminal
/-!
# The Factorisati... |
CategoryTheory\Category\GaloisConnection.lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison, Johannes Hölzl, Reid Barton
-/
import Mathlib.CategoryTheory.Category.Preorder
import Mathlib.CategoryTheory.Adjunction.Basic
import Mathlib.Order.Galoi... |
CategoryTheory\Category\Grpd.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.CategoryTheory.SingleObj
import Mathlib.CategoryTheory.Limits.Shapes.Products
/-!
# Category of groupoids
This file contains the definition of the ... |
CategoryTheory\Category\Init.lean | /-
Copyright (c) 2023 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg
-/
import Aesop
/-!
# Category Theory Rule Set
This module defines the `CategoryTheory` Aesop rule set which is used by the
`aesop_cat` tactic. Aesop rule sets only b... |
CategoryTheory\Category\KleisliCat.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.CategoryTheory.Category.Basic
/-!
# The Kleisli construction on the Type category
Define the Kleisli category for (control) monads.
`CategoryTheory/Monad/... |
CategoryTheory\Category\Pairwise.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Order.CompleteLattice
import Mathlib.CategoryTheory.Category.Preorder
import Mathlib.CategoryTheory.Limits.IsLimit
/-!
# The category of "pairwise int... |
CategoryTheory\Category\PartialFun.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.CategoryTheory.Category.Pointed
import Mathlib.Data.PFun
/-!
# The category of types with partial functions
This defines `PartialFun`, the category of ty... |
CategoryTheory\Category\Pointed.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.CategoryTheory.ConcreteCategory.Basic
import Mathlib.CategoryTheory.Adjunction.Basic
/-!
# The category of pointed types
This defines `Pointed`, the cate... |
CategoryTheory\Category\Preorder.lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison, Johannes Hölzl, Reid Barton
-/
import Mathlib.CategoryTheory.Equivalence
import Mathlib.CategoryTheory.EqToHom
import Mathlib.Order.Hom.Basic
import Mat... |
CategoryTheory\Category\Quiv.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.CategoryTheory.Adjunction.Basic
import Mathlib.CategoryTheory.Category.Cat
import Mathlib.CategoryTheory.PathCategory
/-!
# The category of quivers
T... |
CategoryTheory\Category\RelCat.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Uni Marx
-/
import Mathlib.CategoryTheory.Iso
import Mathlib.CategoryTheory.EssentialImage
import Mathlib.CategoryTheory.Types
import Mathlib.CategoryTheory.Opposites
i... |
CategoryTheory\Category\TwoP.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.CategoryTheory.Category.Bipointed
import Mathlib.Data.TwoPointing
/-!
# The category of two-pointed types
This defines `TwoP`, the category of two-pointe... |
CategoryTheory\Category\ULift.lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import Mathlib.CategoryTheory.Category.Basic
import Mathlib.CategoryTheory.Equivalence
import Mathlib.CategoryTheory.EqToHom
import Mathlib.Data.ULift
/-!
# Basic API for UL... |
CategoryTheory\Category\Cat\Adjunction.lean | /-
Copyright (c) 2024 Nicolas Rolland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolas Rolland
-/
import Mathlib.CategoryTheory.Category.Cat
import Mathlib.CategoryTheory.Adjunction.Basic
/-!
# Adjunctions related to Cat, the category of categories
The embeddin... |
CategoryTheory\Category\Cat\Limit.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.CategoryTheory.Category.Cat
import Mathlib.CategoryTheory.Limits.Types
import Mathlib.CategoryTheory.Limits.Preserves.Basic
/-!
# The category of smal... |
CategoryTheory\ChosenFiniteProducts\FunctorCategory.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.ChosenFiniteProducts
import Mathlib.CategoryTheory.Limits.FunctorCategory
/-!
# Functor categories have chosen finite products
If `C` is a categ... |
CategoryTheory\Closed\Cartesian.lean | /-
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
-/
import Mathlib.CategoryTheory.EpiMono
import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts
import Mathlib.Cate... |
CategoryTheory\Closed\Functor.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.CategoryTheory.Closed.Cartesian
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Adjunction.FullyFaithful... |
CategoryTheory\Closed\FunctorCategory.lean | /-
Copyright (c) 2022 Antoine Labelle. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle
-/
import Mathlib.CategoryTheory.Closed.Monoidal
import Mathlib.CategoryTheory.Functor.Currying
import Mathlib.CategoryTheory.Monoidal.FunctorCategory
/-!
# Functors ... |
CategoryTheory\Closed\Ideal.lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts
import Mathlib.Cate... |
CategoryTheory\Closed\Monoidal.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Monoidal.Functor
import Mathlib.CategoryTheory.Adjunction.Limits
import Mathlib.CategoryTheory.Adjunction.Mates
/-!
# Clo... |
CategoryTheory\Closed\Types.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.CategoryTheory.Limits.Presheaf
import Mathlib.CategoryTheory.Limits.Preserves.FunctorCategory
import Mathlib.CategoryTheory.Limits.Shapes.Types
import Math... |
CategoryTheory\Closed\Zero.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.CategoryTheory.Closed.Cartesian
import Mathlib.CategoryTheory.PUnit
import Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects
/-!
# A cartesian closed categ... |
CategoryTheory\Comma\Arrow.lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Comma.Basic
/-!
# The category of arrows
The category of arrows, with morphisms commutative squares.
We set this up as a specialization ... |
CategoryTheory\Comma\Basic.lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johan Commelin, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Iso
import Mathlib.CategoryTheory.Functor.Category
import Mathlib.CategoryTheory.EqToHom
/-!
# Comma cate... |
CategoryTheory\Comma\Over.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Comma.StructuredArrow
import Mathlib.CategoryTheory.PUnit
import Mathlib.CategoryTheory.Functor.ReflectsIso
import Mathlib... |
CategoryTheory\Comma\Presheaf.lean | /-
Copyright (c) 2024 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Comma.Over
import Mathlib.Tactic.CategoryTheory.Elementwise
/-!
# Computation of `Over A` for a presheaf `A`
Let `A : Cᵒᵖ ⥤ Type v` be a... |
CategoryTheory\Comma\StructuredArrow.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Scott Morrison
-/
import Mathlib.CategoryTheory.Comma.Basic
import Mathlib.CategoryTheory.PUnit
import Mathlib.CategoryTheory.Limits.Shapes.Terminal
import Mathlib.Category... |
CategoryTheory\ConcreteCategory\Basic.lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johannes Hölzl, Reid Barton, Sean Leather, Yury Kudryashov
-/
import Mathlib.CategoryTheory.Types
/-!
# Concrete categories
A concrete category is a category `C` with... |
CategoryTheory\ConcreteCategory\Bundled.lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johannes Hölzl, Reid Barton, Sean Leather
-/
import Batteries.Tactic.Lint.Misc
/-!
# Bundled types
`Bundled c` provides a uniform structure for bundling a type equipp... |
CategoryTheory\ConcreteCategory\BundledHom.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Yury Kudryashov
-/
import Mathlib.CategoryTheory.ConcreteCategory.Basic
import Mathlib.CategoryTheory.ConcreteCategory.Bundled
/-!
# Category instances for algebraic s... |
CategoryTheory\ConcreteCategory\Elementwise.lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.Tactic.CategoryTheory.Elementwise
import Mathlib.CategoryTheory.Limits.HasLimits
import Mathlib.CategoryTheory.Limits.Shapes.Kernels
import Mathlib.CategoryT... |
CategoryTheory\ConcreteCategory\EpiMono.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Limits.Shapes.Images
import Mathlib.CategoryTheory.MorphismProperty.Concrete
import Mathlib.CategoryTheory.Types
import Mathlib.CategoryTheory.Lim... |
CategoryTheory\ConcreteCategory\ReflectsIso.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.CategoryTheory.ConcreteCategory.Basic
import Mathlib.CategoryTheory.Functor.ReflectsIso
/-!
A `forget₂ C D` forgetful functor between concrete categor... |
CategoryTheory\ConcreteCategory\UnbundledHom.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.CategoryTheory.ConcreteCategory.BundledHom
/-!
# Category instances for structures that use unbundled homs
This file provides basic infrastructure ... |
CategoryTheory\Dialectica\Basic.lean | /-
Copyright (c) 2024 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.CategoryTheory.Subobject.Basic
import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts
/-!
# Dialectica category
We define the category `Dial` of ... |
CategoryTheory\Dialectica\Monoidal.lean | /-
Copyright (c) 2024 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.CategoryTheory.Subobject.Lattice
import Mathlib.CategoryTheory.Monoidal.Braided.Basic
import Mathlib.CategoryTheory.Dialectica.Basic
/-!
# The Dialect... |
CategoryTheory\EffectiveEpi\Basic.lean | /-
Copyright (c) 2023 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import Mathlib.CategoryTheory.Limits.Shapes.Products
/-!
# Effective epimorphisms
We define the notion of effective epimorphism and effective epimorphic family of morphisms... |
CategoryTheory\EffectiveEpi\Comp.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.EffectiveEpi.Basic
/-!
# Composition of effective epimorphisms
This file provides `EffectiveEpi` instances for certain composition... |
CategoryTheory\EffectiveEpi\Coproduct.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.EffectiveEpi.Basic
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
import Mathlib.Tactic.ApplyFun
/-!
# Effective ... |
CategoryTheory\EffectiveEpi\Enough.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.EffectiveEpi.Basic
/-!
# Effectively enough objects in the image of a functor
We define the class `F.EffectivelyEnough` on a funct... |
CategoryTheory\EffectiveEpi\Extensive.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.EffectiveEpi.Preserves
import Mathlib.CategoryTheory.EffectiveEpi.Coproduct
import Mathlib.CategoryTheory.Extensive
import Mathlib.C... |
CategoryTheory\EffectiveEpi\Preserves.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.EffectiveEpi.Comp
import Mathlib.Data.Fintype.Card
/-!
# Functors preserving effective epimorphisms
This file concerns functors wh... |
CategoryTheory\EffectiveEpi\RegularEpi.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.Limits.Shapes.RegularMono
import Mathlib.CategoryTheory.EffectiveEpi.Basic
/-!
# The relationship between effective and regular epi... |
CategoryTheory\Endofunctor\Algebra.lean | /-
Copyright (c) 2022 Joseph Hua. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta, Johan Commelin, Reid Barton, Rob Lewis, Joseph Hua
-/
import Mathlib.CategoryTheory.Limits.Shapes.Terminal
/-!
# Algebras of endofunctors
This file defines... |
CategoryTheory\Enriched\Basic.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.CategoryTheory.Monoidal.Types.Symmetric
import Mathlib.CategoryTheory.Monoidal.Types.Coyoneda
import Mathlib.CategoryTheory.Monoidal.Center
import Math... |
CategoryTheory\FiberedCategory\BasedCategory.lean | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Lezeau, Calle Sönne
-/
import Mathlib.CategoryTheory.FiberedCategory.HomLift
import Mathlib.CategoryTheory.Bicategory.Strict
import Mathlib.CategoryTheory.Functor.Category
import Ma... |
CategoryTheory\FiberedCategory\Cartesian.lean | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Lezeau, Calle Sönne
-/
import Mathlib.CategoryTheory.FiberedCategory.HomLift
/-!
# Cartesian morphisms
This file defines cartesian resp. strongly cartesian morphisms with respect ... |
CategoryTheory\FiberedCategory\HomLift.lean | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Lezeau, Calle Sönne
-/
import Mathlib.CategoryTheory.Functor.Category
import Mathlib.CategoryTheory.CommSq
/-!
# HomLift
Given a functor `p : 𝒳 ⥤ 𝒮`, this file provides API for... |
CategoryTheory\Filtered\Basic.lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Scott Morrison
-/
import Mathlib.CategoryTheory.FinCategory.Basic
import Mathlib.CategoryTheory.Limits.Cones
import Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits
import M... |
CategoryTheory\Filtered\Connected.lean | /-
Copyright (c) 2024 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Filtered.Basic
import Mathlib.CategoryTheory.IsConnected
/-!
# Filtered categories are connected
-/
universe v u
namespace CategoryTheo... |
CategoryTheory\Filtered\Final.lean | /-
Copyright (c) 2024 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Filtered.Connected
import Mathlib.CategoryTheory.Limits.TypesFiltered
import Mathlib.CategoryTheory.Limits.Final
/-!
# Final functors wit... |
CategoryTheory\Filtered\Small.lean | /-
Copyright (c) 2023 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.EssentiallySmall
import Mathlib.CategoryTheory.Filtered.Basic
/-!
# A functor from a small category to a filtered category factors throug... |
CategoryTheory\FinCategory\AsType.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Data.Fintype.Card
import Mathlib.CategoryTheory.FinCategory.Basic
/-!
# Finite categories are equivalent to category in `Type 0`.
-/
universe w v u
... |
CategoryTheory\FinCategory\Basic.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Data.Fintype.Basic
import Mathlib.CategoryTheory.DiscreteCategory
import Mathlib.CategoryTheory.Opposites
import Mathlib.CategoryTheory.Category.ULift
... |
CategoryTheory\Functor\Basic.lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baumann, Stephen Morgan, Scott Morrison
-/
import Mathlib.CategoryTheory.Category.Basic
/-!
# Functors
Defines a functor between categories, extending a `Prefunctor` between quiv... |
CategoryTheory\Functor\Category.lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baumann, Stephen Morgan, Scott Morrison, Floris van Doorn
-/
import Mathlib.CategoryTheory.NatTrans
import Mathlib.CategoryTheory.Iso
/-!
# The category of functors and natural tr... |
CategoryTheory\Functor\Const.lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Opposites
/-!
# The constant functor
`const J : C ⥤ (J ⥤ C)` is the functor that sends an object `X : C` to the functor ... |
CategoryTheory\Functor\Currying.lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.CategoryTheory.Products.Basic
/-!
# Curry and uncurry, as functors.
We define `curry : ((C × D) ⥤ E) ⥤ (C ⥤ (D ⥤ E))` and `uncurry : (C ⥤ (D ⥤ E)) ⥤ ... |
CategoryTheory\Functor\EpiMono.lean | /-
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.EpiMono
import Mathlib.CategoryTheory.Limits.Shapes.StrongEpi
import Mathlib.CategoryTheory.LiftingProperties.Adjunction
/-!
# Preservati... |
CategoryTheory\Functor\Flat.lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.CategoryTheory.Limits.ConeCategory
import Mathlib.CategoryTheory.Limits.FilteredColimitCommutesFiniteLimit
import Mathlib.CategoryTheory.Limits.Preserves.Fil... |
CategoryTheory\Functor\FullyFaithful.lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.CategoryTheory.NatIso
import Mathlib.Logic.Equiv.Defs
/-!
# Full and faithful functors
We define typeclasses `Full` and `Faithful`, decorating functo... |
CategoryTheory\Functor\Functorial.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.CategoryTheory.Functor.Basic
/-!
# Unbundled functors, as a typeclass decorating the object-level function.
-/
namespace CategoryTheory
-- declare ... |
CategoryTheory\Functor\Hom.lean | /-
Copyright (c) 2018 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Scott Morrison
-/
import Mathlib.CategoryTheory.Products.Basic
import Mathlib.CategoryTheory.Types
/-!
The hom functor, sending `(X, Y)` to the type `X ⟶ Y`.
-/
universe v... |
CategoryTheory\Functor\OfSequence.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Order.Group.Nat
import Mathlib.CategoryTheory.Category.Preorder
import Mathlib.CategoryTheory.EqToHom
/-!
# Functors from the category of the ordered se... |
CategoryTheory\Functor\ReflectsIso.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.CategoryTheory.Balanced
import Mathlib.CategoryTheory.Functor.EpiMono
import Mathlib.CategoryTheory.Functor.FullyFaithful
/-!
# Functors which reflect iso... |
CategoryTheory\Functor\Trifunctor.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Functor.Category
/-!
# Trifunctors obtained by composition of bifunctors
Given two bifunctors `F₁₂ : C₁ ⥤ C₂ ⥤ C₁₂` and `G : C₁₂ ⥤ C₃ ⥤ C₄`, we d... |
CategoryTheory\Functor\Derived\RightDerived.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Functor.KanExtension.Basic
import Mathlib.CategoryTheory.Localization.Predicate
/-!
# Right derived functors
In this file, given a functor `F : ... |
CategoryTheory\Functor\KanExtension\Adjunction.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Functor.KanExtension.Pointwise
/-! # The Kan extension functor
Given a functor `L : C ⥤ D`, we define the left Kan extension functor
`L.lan : (C... |
CategoryTheory\Functor\KanExtension\Basic.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Comma.StructuredArrow
import Mathlib.CategoryTheory.Limits.Shapes.Equivalence
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal
/-!
... |
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