path stringlengths 11 71 | content stringlengths 75 124k |
|---|---|
CategoryTheory\Functor\KanExtension\Pointwise.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
/-!
# Pointwise Kan extensions
In this file, we define the notion of pointwise (left) Kan extension. Given two functo... |
CategoryTheory\Galois\Basic.lean | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.CategoryTheory.FintypeCat
import Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers
import Mathlib.CategoryTheory.Limits.Fin... |
CategoryTheory\Galois\Decomposition.lean | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.CategoryTheory.Galois.GaloisObjects
import Mathlib.CategoryTheory.Limits.Shapes.CombinedProducts
/-!
# Decomposition of objects into connected com... |
CategoryTheory\Galois\Examples.lean | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.CategoryTheory.Galois.Basic
import Mathlib.RepresentationTheory.Action.Basic
import Mathlib.RepresentationTheory.Action.Concrete
import Mathlib.Rep... |
CategoryTheory\Galois\GaloisObjects.lean | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.CategoryTheory.Galois.Basic
import Mathlib.CategoryTheory.Limits.FintypeCat
import Mathlib.CategoryTheory.Limits.Preserves.Limits
import Mathlib.Ca... |
CategoryTheory\Galois\Prorepresentability.lean | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.Algebra.Category.Grp.Limits
import Mathlib.CategoryTheory.CofilteredSystem
import Mathlib.CategoryTheory.Galois.Decomposition
import Mathlib.Catego... |
CategoryTheory\GradedObject\Associator.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.GradedObject.Trifunctor
/-!
# The associator for actions of bifunctors on graded objects
Given functors `F₁₂ : C₁ ⥤ C₂ ⥤ C₁₂`, `G : C₁₂ ⥤ C₃ ⥤ C... |
CategoryTheory\GradedObject\Bifunctor.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.GradedObject
/-!
# The action of bifunctors on graded objects
Given a bifunctor `F : C₁ ⥤ C₂ ⥤ C₃` and types `I` and `J`, we construct an obvious... |
CategoryTheory\GradedObject\Monoidal.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Kim Morrison
-/
import Mathlib.CategoryTheory.GradedObject.Unitor
import Mathlib.Data.Fintype.Prod
/-!
# The monoidal category structures on graded objects
Assuming that `C` is... |
CategoryTheory\GradedObject\Single.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.GradedObject
/-!
# The graded object in a single degree
In this file, we define the functor `GradedObject.single j : C ⥤ GradedObject J C`
which... |
CategoryTheory\GradedObject\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.GradedObject.Bifunctor
import Mathlib.CategoryTheory.Functor.Trifunctor
/-!
# The action of trifunctors on graded objects
Given a trifunctor `F. ... |
CategoryTheory\GradedObject\Unitor.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.GradedObject.Associator
import Mathlib.CategoryTheory.GradedObject.Single
/-!
# The left and right unitors
Given a bifunctor `F : C ⥤ D ⥤ D`, an ... |
CategoryTheory\Groupoid\Basic.lean | /-
Copyright (c) 2022 Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémi Bottinelli
-/
import Mathlib.CategoryTheory.Groupoid
import Mathlib.Combinatorics.Quiver.Basic
/-!
This file defines a few basic properties of groupoids.
-/
namespace CategoryT... |
CategoryTheory\Groupoid\FreeGroupoid.lean | /-
Copyright (c) 2022 Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémi Bottinelli
-/
import Mathlib.CategoryTheory.Category.Basic
import Mathlib.CategoryTheory.Functor.Basic
import Mathlib.CategoryTheory.Groupoid
import Mathlib.Tactic.NthRewrite
imp... |
CategoryTheory\Groupoid\Subgroupoid.lean | /-
Copyright (c) 2022 Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémi Bottinelli, Junyan Xu
-/
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.CategoryTheory.Groupoid.VertexGroup
import Mathlib.CategoryTheory.Groupoid.Basic
import Mathli... |
CategoryTheory\Groupoid\VertexGroup.lean | /-
Copyright (c) 2022 Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémi Bottinelli
-/
import Mathlib.Algebra.Group.Equiv.Basic
import Mathlib.CategoryTheory.Groupoid
import Mathlib.CategoryTheory.PathCategory
import Mathlib.Combinatorics.Quiver.Path
... |
CategoryTheory\GuitartExact\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.Limits.Final
/-!
# Guitart exact squares
Given four functors `T`, `L`, `R` and `B`, a 2-square `TwoSquare T L R B` consists of
a natural transfo... |
CategoryTheory\GuitartExact\VerticalComposition.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.CatCommSq
import Mathlib.CategoryTheory.GuitartExact.Basic
/-!
# Vertical composition of Guitart exact squares
In this file, we show that the ve... |
CategoryTheory\Idempotents\Basic.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Abelian.Basic
/-!
# Idempotent complete categories
In this file, we define the notion of idempotent complete categories
(also known as Karoubian... |
CategoryTheory\Idempotents\Biproducts.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Idempotents.Karoubi
/-!
# Biproducts in the idempotent completion of a preadditive category
In this file, we define an instance expressing that... |
CategoryTheory\Idempotents\FunctorCategories.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Idempotents.Karoubi
/-!
# Idempotent completeness and functor categories
In this file we define an instance `functor_category_isIdempotentComple... |
CategoryTheory\Idempotents\FunctorExtension.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Idempotents.Karoubi
/-!
# Extension of functors to the idempotent completion
In this file, we construct an extension `functorExtension₁`
of func... |
CategoryTheory\Idempotents\HomologicalComplex.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Homology.Additive
import Mathlib.CategoryTheory.Idempotents.Karoubi
/-!
# Idempotent completeness and homological complexes
This file contains simplifi... |
CategoryTheory\Idempotents\Karoubi.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Idempotents.Basic
import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
import Mathlib.CategoryTheory.Equivalence
/-!
# The Karoubi envelope ... |
CategoryTheory\Idempotents\KaroubiKaroubi.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Idempotents.Karoubi
/-!
# Idempotence of the Karoubi envelope
In this file, we construct the equivalence of categories
`KaroubiKaroubi.equivalen... |
CategoryTheory\Idempotents\SimplicialObject.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.SimplicialObject
import Mathlib.CategoryTheory.Idempotents.FunctorCategories
/-!
# Idempotent completeness of categories of simplicial object... |
CategoryTheory\LiftingProperties\Adjunction.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.LiftingProperties.Basic
import Mathlib.CategoryTheory.Adjunction.Basic
/-!
# Lifting properties and adjunction
In this file, we obtain `Adjunct... |
CategoryTheory\LiftingProperties\Basic.lean | /-
Copyright (c) 2021 Jakob Scholbach. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob Scholbach, Joël Riou
-/
import Mathlib.CategoryTheory.CommSq
/-!
# Lifting properties
This file defines the lifting property of two morphisms in a category and
shows basic pro... |
CategoryTheory\Limits\Bicones.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.Cones
import Mathlib.CategoryTheory.FinCategory.Basic
/-!
# Bicones
Given a category `J`, a walking `Bicone J` is a category whose ob... |
CategoryTheory\Limits\ColimitLimit.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.Limits.Types
import Mathlib.CategoryTheory.Functor.Currying
import Mathlib.CategoryTheory.Limits.FunctorCategory
/-!
# The morphism com... |
CategoryTheory\Limits\Comma.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.Comma.Arrow
import Mathlib.CategoryTheory.Comma.StructuredArrow
import Mathlib.CategoryTheory.Limits.Constructions.EpiMono
import Mathlib.Ca... |
CategoryTheory\Limits\ConeCategory.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.Adjunction.Comma
import Mathlib.CategoryTheory.Comma.Over
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal
import Mathlib.Catego... |
CategoryTheory\Limits\Cones.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, Floris van Doorn
-/
import Mathlib.CategoryTheory.Functor.Const
import Mathlib.CategoryTheory.DiscreteCategory
import Mathlib.CategoryTheory.Yoneda
impo... |
CategoryTheory\Limits\Connected.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.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
import Mathlib.CategoryTheory.Limits.Shapes.WidePullback... |
CategoryTheory\Limits\Creates.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.Preserves.Basic
/-!
# Creating (co)limits
We say that `F` creates limits of `K` if, given any limit cone `c` for `K ⋙ F`
(i.e. belo... |
CategoryTheory\Limits\Elements.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.Elements
import Mathlib.CategoryTheory.Limits.Types
import Mathlib.CategoryTheory.Limits.Creates
import Mathlib.CategoryTheory.Limits.Pres... |
CategoryTheory\Limits\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.Pullback.CommSq
/-!
# Relation between mono/epi and pullback/pushout squares
In this file, monomorphisms and epimorphisms are char... |
CategoryTheory\Limits\EssentiallySmall.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.Limits.Shapes.Products
import Mathlib.CategoryTheory.EssentiallySmall
/-!
# Limits over essentially small indexing categories
If `C` has... |
CategoryTheory\Limits\ExactFunctor.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.Limits.Preserves.Finite
/-!
# Bundled exact functors
We say that a functor `F` is left exact if it preserves finite limits, it is right ... |
CategoryTheory\Limits\Filtered.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.Filtered.Basic
import Mathlib.CategoryTheory.Limits.HasLimits
import Mathlib.CategoryTheory.Limits.Types
/-!
# Filtered categories and li... |
CategoryTheory\Limits\FilteredColimitCommutesFiniteLimit.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.Limits.ColimitLimit
import Mathlib.CategoryTheory.Limits.Preserves.FunctorCategory
import Mathlib.CategoryTheory.Limits.Preserves.Finite... |
CategoryTheory\Limits\Final.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.Comma.StructuredArrow
import Mathlib.CategoryTheory.IsConnected
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal
import Ma... |
CategoryTheory\Limits\FinallySmall.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.Filtered.Final
/-!
# Finally small categories
A category given by `(J : Type u) [Category.{v} J]` is `w`-finally small if there exists a... |
CategoryTheory\Limits\FintypeCat.lean | /-
Copyright (c) 2023 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.CategoryTheory.FintypeCat
import Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits
import Mathlib.CategoryTheory.Limits.Types
import Mathlib.Catego... |
CategoryTheory\Limits\Fubini.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.Limits.HasLimits
import Mathlib.CategoryTheory.Products.Basic
import Mathlib.CategoryTheory.Functor.Currying
import Mathlib.CategoryTheo... |
CategoryTheory\Limits\FullSubcategory.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.Limits.Creates
/-!
# Limits in full subcategories
We introduce the notion of a property closed under taking limits and show that if `P` ... |
CategoryTheory\Limits\FunctorCategory.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.Functor.Currying
import Mathlib.CategoryTheory.Limits.Preserves.Limits
/-!
# (Co)limits in functor categories.
We show that if `D` has... |
CategoryTheory\Limits\FunctorToTypes.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.Limits.FunctorCategory
import Mathlib.CategoryTheory.Limits.Types
/-!
# Concrete description of (co)limits in functor categories
Some of... |
CategoryTheory\Limits\HasLimits.lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Mario Carneiro, Scott Morrison, Floris van Doorn
-/
import Mathlib.CategoryTheory.Limits.IsLimit
import Mathlib.CategoryTheory.Category.ULift
import Mathlib.CategoryTheory... |
CategoryTheory\Limits\IndYoneda.lean | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.CategoryTheory.Limits.Opposites
import Mathlib.CategoryTheory.Limits.Preserves.Limits
import Mathlib.CategoryTheory.Limits.Yoneda
/-!
# Ind- and ... |
CategoryTheory\Limits\IsConnected.lean | /-
Copyright (c) 2024 Paul Reichert. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Reichert
-/
import Mathlib.CategoryTheory.Limits.Types
import Mathlib.CategoryTheory.IsConnected
import Mathlib.CategoryTheory.Limits.Final
import Mathlib.CategoryTheory.HomCongr
... |
CategoryTheory\Limits\IsLimit.lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Mario Carneiro, Scott Morrison, Floris van Doorn
-/
import Mathlib.CategoryTheory.Adjunction.Basic
import Mathlib.CategoryTheory.Limits.Cones
import Batteries.Tactic.Congr... |
CategoryTheory\Limits\Lattice.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Justus Springer
-/
import Mathlib.Order.CompleteLattice
import Mathlib.Data.Finset.Lattice
import Mathlib.CategoryTheory.Category.Preorder
import Mathlib.CategoryTheory... |
CategoryTheory\Limits\MonoCoprod.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.ConcreteCategory.Basic
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Limits.Shapes.RegularMon... |
CategoryTheory\Limits\Opposites.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Floris van Doorn
-/
import Mathlib.CategoryTheory.Limits.Filtered
import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts
import Mathlib.CategoryTheory.Limits.Shapes... |
CategoryTheory\Limits\Over.lean | /-
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
-/
import Mathlib.CategoryTheory.Comma.Over
import Mathlib.CategoryTheory.Limits.Comma
import Mathlib.CategoryTheory.Limits.ConeCategory
impor... |
CategoryTheory\Limits\Pi.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.Pi.Basic
import Mathlib.CategoryTheory.Limits.HasLimits
/-!
# Limits in the category of indexed families of objects.
Given a functor `... |
CategoryTheory\Limits\Presheaf.lean | /-
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
-/
import Mathlib.CategoryTheory.Comma.Presheaf
import Mathlib.CategoryTheory.Elements
import Mathlib.CategoryTheory.Functor.KanExtension.Adjunction
import Mathli... |
CategoryTheory\Limits\SmallComplete.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.Shapes.Products
import Mathlib.SetTheory.Cardinal.Basic
/-!
# Any small complete category is a preorder
We show that any small cate... |
CategoryTheory\Limits\Types.lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Reid Barton
-/
import Mathlib.Data.TypeMax
import Mathlib.Logic.UnivLE
import Mathlib.CategoryTheory.Limits.Shapes.Images
/-!
# Limits in the category of types.
We sh... |
CategoryTheory\Limits\TypesFiltered.lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Reid Barton
-/
import Mathlib.CategoryTheory.Limits.Types
import Mathlib.CategoryTheory.Filtered.Basic
/-!
# Filtered colimits in the category of types.
We give a cha... |
CategoryTheory\Limits\Unit.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.PUnit
import Mathlib.CategoryTheory.Limits.HasLimits
/-!
# `Discrete PUnit` has limits and colimits
Mostly for the sake of constructin... |
CategoryTheory\Limits\VanKampen.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.CategoryTheory.Adjunction.FullyFaithful
import Mathlib.CategoryTheory.Adjunction.Limits
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Ma... |
CategoryTheory\Limits\Yoneda.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.Limits.FunctorCategory
import Mathlib.CategoryTheory.Limits.Types
import Mathlib.Util.AssertExists
/-!
# Limit properties... |
CategoryTheory\Limits\ConcreteCategory\Basic.lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Adam Topaz
-/
import Mathlib.CategoryTheory.ConcreteCategory.Basic
import Mathlib.CategoryTheory.Limits.Preserves.Basic
import Mathlib.CategoryTheory.Limits.TypesFilter... |
CategoryTheory\Limits\ConcreteCategory\WithAlgebraicStructures.lean | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic
import Mathlib.Algebra.Module.LinearMap.Defs
import Mathlib.Tactic.CategoryTheory.Elementwise
/-!
# Colimits... |
CategoryTheory\Limits\Constructions\BinaryProducts.lean | /-
Copyright (c) 2020 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.Limits.Shapes.Terminal
import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Limits.Preserve... |
CategoryTheory\Limits\Constructions\EpiMono.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.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono
import Mathlib.CategoryTheory.Limits.Preserves.Shapes... |
CategoryTheory\Limits\Constructions\Equalizers.lean | /-
Copyright (c) 2020 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.Limits.Shapes.Equalizers
import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Limits.Preser... |
CategoryTheory\Limits\Constructions\Filtered.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.Limits.Constructions.LimitsOfProductsAndEqualizers
import Mathlib.CategoryTheory.Limits.Opposites
/-!
# Constructing colimits from finite... |
CategoryTheory\Limits\Constructions\FiniteProductsOfBinaryProducts.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.Preserves.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products
import Mathlib.CategoryTheory.Limits.S... |
CategoryTheory\Limits\Constructions\LimitsOfProductsAndEqualizers.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Scott Morrison
-/
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.Fintype.Sigma
import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
import Mathlib.CategoryTheory.Li... |
CategoryTheory\Limits\Constructions\Pullbacks.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.Limits.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.H... |
CategoryTheory\Limits\Constructions\WeaklyInitial.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.Shapes.WideEqualizers
import Mathlib.CategoryTheory.Limits.Shapes.Products
import Mathlib.CategoryTheory.Limits.Shapes.Terminal
/-!
... |
CategoryTheory\Limits\Constructions\ZeroObjects.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.Limits.Shapes.ZeroMorphisms
import Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts
/-!
# Limits involving zero objects
Bina... |
CategoryTheory\Limits\Constructions\Over\Basic.lean | /-
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
-/
import Mathlib.CategoryTheory.Limits.Connected
import Mathlib.CategoryTheory.Limits.Constructions.Over.Products
import Mathlib.CategoryTheo... |
CategoryTheory\Limits\Constructions\Over\Connected.lean | /-
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
-/
import Mathlib.CategoryTheory.Limits.Creates
import Mathlib.CategoryTheory.Comma.Over
import Mathlib.CategoryTheory.IsConnected
/-!
# Conn... |
CategoryTheory\Limits\Constructions\Over\Products.lean | /-
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
-/
import Mathlib.CategoryTheory.Comma.Over
import Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks
import Mathlib.CategoryTheory.Limits.Sha... |
CategoryTheory\Limits\Final\ParallelPair.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Joël Riou
-/
import Mathlib.CategoryTheory.Limits.Final
/-!
# Conditions for `parallelPair` to be initial
In this file we give sufficient conditions on a category... |
CategoryTheory\Limits\Indization\IndObject.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.Limits.FinallySmall
import Mathlib.CategoryTheory.Limits.Presheaf
import Mathlib.CategoryTheory.Filtered.Small
/-!
# Ind-objects
For a p... |
CategoryTheory\Limits\Preserves\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, Reid Barton, Bhavik Mehta, Jakob von Raumer
-/
import Mathlib.CategoryTheory.Limits.HasLimits
/-!
# Preservation and reflection of (co)limits.
There are various disti... |
CategoryTheory\Limits\Preserves\Filtered.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Justus Springer
-/
import Mathlib.CategoryTheory.Limits.Preserves.Basic
import Mathlib.CategoryTheory.Filtered.Basic
/-!
# Preservation of filtered colimits and cofilt... |
CategoryTheory\Limits\Preserves\Finite.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.Preserves.Basic
import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts
/-!
# Preservation of finite (co)limits.
These functors ar... |
CategoryTheory\Limits\Preserves\FunctorCategory.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.FunctorCategory
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Limits.Yoneda
impo... |
CategoryTheory\Limits\Preserves\Limits.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.Limits.Preserves.Basic
/-!
# Isomorphisms about functors which preserve (co)limits
If `G` preserves limits, and `C` and ... |
CategoryTheory\Limits\Preserves\Opposites.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.Limits.Opposites
import Mathlib.CategoryTheory.Limits.Preserves.Finite
/-!
# Limit preservation properties of `functor.op` and related co... |
CategoryTheory\Limits\Preserves\Ulift.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Junyan Xu
-/
import Mathlib.CategoryTheory.Limits.Creates
import Mathlib.CategoryTheory.Limits.Types
import Mathlib.Data.Set.Subsingleton
/-!
# `ULift` creates sma... |
CategoryTheory\Limits\Preserves\Shapes\BinaryProducts.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.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Limits.Preserves.Basic
/-!
# Preserving binary products
Constructions to relate... |
CategoryTheory\Limits\Preserves\Shapes\Biproducts.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.Limits.Shapes.Biproducts
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero
/-!
# Preservation of biproducts
We define the image... |
CategoryTheory\Limits\Preserves\Shapes\Equalizers.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.Shapes.SplitCoequalizer
import Mathlib.CategoryTheory.Limits.Shapes.SplitEqualizer
import Mathlib.CategoryTheory.Limits.Preserves.Bas... |
CategoryTheory\Limits\Preserves\Shapes\Images.lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import Mathlib.CategoryTheory.Limits.Shapes.Images
import Mathlib.CategoryTheory.Limits.Constructions.EpiMono
/-!
# Preserving images
In this file, we show that if a fu... |
CategoryTheory\Limits\Preserves\Shapes\Kernels.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.Limits.Shapes.Kernels
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero
/-!
# Preserving (co)kernels
Constructions to relate ... |
CategoryTheory\Limits\Preserves\Shapes\Products.lean | /-
Copyright (c) 2020 Scott Morrison, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Limits.Shapes.Products
import Mathlib.CategoryTheory.Limits.Preserves.Basic
/-!
# Preserving products
Cons... |
CategoryTheory\Limits\Preserves\Shapes\Pullbacks.lean | /-
Copyright (c) 2020 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.Limits.Shapes.Pullback.HasPullback
import Mathlib.CategoryTheory.Limits.Preserves.Basic
import Mathlib.CategoryTheory.Limits.Op... |
CategoryTheory\Limits\Preserves\Shapes\Square.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.Pullback.Square
import Mathlib.CategoryTheory.Limits.Yoneda
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks
/-!
# P... |
CategoryTheory\Limits\Preserves\Shapes\Terminal.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.Shapes.Terminal
import Mathlib.CategoryTheory.Limits.Preserves.Basic
/-!
# Preserving terminal object
Constructions to relate the n... |
CategoryTheory\Limits\Preserves\Shapes\Zero.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.Limits.Preserves.Shapes.Terminal
import Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms
/-!
# Preservation of zero objects and zero mo... |
CategoryTheory\Limits\Shapes\BinaryProducts.lean | /-
Copyright (c) 2019 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.Comma.Over
import Mathlib.CategoryTheory.DiscreteCategory
import Mathlib.CategoryTheory.EpiMono
import Mathlib.CategoryThe... |
CategoryTheory\Limits\Shapes\Biproducts.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Jakob von Raumer
-/
import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts
import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
import Mathlib.CategoryTheory.... |
CategoryTheory\Limits\Shapes\CombinedProducts.lean | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.CategoryTheory.Limits.Shapes.Products
import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
/-!
# Constructors for combining (co)fans
We pro... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.