path stringlengths 11 71 | content stringlengths 75 124k |
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CategoryTheory\Limits\Shapes\ConcreteCategory.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Scott Morrison, Adam Topaz
-/
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products
import Mathlib.C... |
CategoryTheory\Limits\Shapes\Countable.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.Final
import Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits
import Mathlib.CategoryTheory.Countable
import Mathlib.Data.Co... |
CategoryTheory\Limits\Shapes\Diagonal.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.Over
import Mathlib.CategoryTheory.Limits.Shapes.KernelPair
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Math... |
CategoryTheory\Limits\Shapes\DisjointCoproduct.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.HasPullback
/-!
# Disjoint coproducts
Defines disjoint c... |
CategoryTheory\Limits\Shapes\Equalizers.lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel
-/
import Mathlib.CategoryTheory.EpiMono
import Mathlib.CategoryTheory.Limits.HasLimits
/-!
# Equalizers and coequalizers
This file defines (co)equalize... |
CategoryTheory\Limits\Shapes\Equivalence.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.Adjunction.Limits
import Mathlib.CategoryTheory.Limits.Shapes.Terminal
/-!
# Transporting existence of specific limits across equivalence... |
CategoryTheory\Limits\Shapes\FiniteLimits.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.FinCategory.AsType
import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
imp... |
CategoryTheory\Limits\Shapes\FiniteProducts.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.Limits.Shapes.FiniteLimits
import Mathlib.CategoryTheory.Limits.Shapes.Products
/-!
# Categories with finite (co)products
Typeclasses ... |
CategoryTheory\Limits\Shapes\FunctorCategory.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.FiniteLimits
import Mathlib.CategoryTheory.Limits.FunctorCategory
/-!
# If `D` has finite (co)limits, so do the functor c... |
CategoryTheory\Limits\Shapes\FunctorToTypes.lean | /-
Copyright (c) 2024 Jack McKoen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jack McKoen
-/
import Mathlib.CategoryTheory.Limits.FunctorCategory
import Mathlib.CategoryTheory.Limits.Types
/-!
# Binary (co)products of type-valued functors
Defines an explicit cons... |
CategoryTheory\Limits\Shapes\Images.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel
-/
import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono
import Mathlib.CategoryTheory.Limits.S... |
CategoryTheory\Limits\Shapes\KernelPair.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.Equalizers
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.RegularMono... |
CategoryTheory\Limits\Shapes\Kernels.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel
-/
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero
/-!
# Kernels and cokernels
In a category with zero morphisms, the kernel of a morphism `f... |
CategoryTheory\Limits\Shapes\Multiequalizer.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.Limits.Shapes.Products
import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
import Mathlib.CategoryTheory.Limits.ConeCategory
/-!
# Multi-(c... |
CategoryTheory\Limits\Shapes\Products.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.Limits.HasLimits
import Mathlib.CategoryTheory.DiscreteCategory
/-!
# Categorical (co)products
This file defines (co)pro... |
CategoryTheory\Limits\Shapes\Reflexive.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.Equalizers
import Mathlib.CategoryTheory.Limits.Shapes.KernelPair
/-!
# Reflexive coequalizers
We define reflexive pairs as ... |
CategoryTheory\Limits\Shapes\RegularMono.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.Shapes.Pullback.HasPullback
import Mathlib.CategoryTheory.Limits.Shapes.StrongEpi
import Mathlib.CategoryTheory.Lim... |
CategoryTheory\Limits\Shapes\SingleObj.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.Types
import Mathlib.CategoryTheory.SingleObj
import Mathlib.GroupTheory.GroupAction.Basic
/-!
# (Co)limits of functors out ... |
CategoryTheory\Limits\Shapes\SplitCoequalizer.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.Equalizers
/-!
# Split coequalizers
We define what it means for a triple of morphisms `f g : X ⟶ Y`, `π : Y ⟶ Z` to be a spl... |
CategoryTheory\Limits\Shapes\SplitEqualizer.lean | /-
Copyright (c) 2024 Jack McKoen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jack McKoen
-/
import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
/-!
# Split Equalizers
We define what it means for a triple of morphisms `f g : X ⟶ Y`, `ι : W ⟶ X` to be a split
e... |
CategoryTheory\Limits\Shapes\StrictInitial.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.Terminal
import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
/-!
# Strict initial objects
This file sets up the basic... |
CategoryTheory\Limits\Shapes\StrongEpi.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.Balanced
import Mathlib.CategoryTheory.LiftingProperties.Basic
/-!
# Strong epimorphisms
In this file, we define strong epimorphisms. A ... |
CategoryTheory\Limits\Shapes\Terminal.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.PEmpty
import Mathlib.CategoryTheory.Limits.HasLimits
import Mathlib.CategoryTheory.EpiMono
import Mathlib.CategoryTheory.... |
CategoryTheory\Limits\Shapes\Types.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.Limits.Shapes.Products
import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
import Math... |
CategoryTheory\Limits\Shapes\WideEqualizers.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.HasLimits
import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
/-!
# Wide equalizers and wide coequalizers
This file defines wide... |
CategoryTheory\Limits\Shapes\WidePullbacks.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Jakob von Raumer
-/
import Mathlib.CategoryTheory.Limits.HasLimits
import Mathlib.CategoryTheory.Thin
/-!
# Wide pullbacks
We define the category `WidePullbackShape`, (re... |
CategoryTheory\Limits\Shapes\ZeroMorphisms.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.Algebra.Group.Pi.Basic
import Mathlib.CategoryTheory.Limits.Shapes.Products
import Mathlib.CategoryTheory.Limits.Shapes.Images
import Mathlib.CategoryT... |
CategoryTheory\Limits\Shapes\ZeroObjects.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johan Commelin
-/
import Mathlib.CategoryTheory.Limits.Shapes.Terminal
/-!
# Zero objects
A category "has a zero object" if it has an object which is both initial and... |
CategoryTheory\Limits\Shapes\NormalMono\Basic.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.Shapes.RegularMono
import Mathlib.CategoryTheory.Limits.Shapes.Kernels
import Mathlib.CategoryTheory.Limits.Preserv... |
CategoryTheory\Limits\Shapes\NormalMono\Equalizers.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.NormalMono.Basic
import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts
/-!
# Normal mono categories with finite produc... |
CategoryTheory\Limits\Shapes\Pullback\Assoc.lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting
/-!
# Associativity of pullbacks
This file shows that pullbacks (and pushouts) are associative up to natu... |
CategoryTheory\Limits\Shapes\Pullback\CommSq.lean | /-
Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Joël Riou, Calle Sönne
-/
import Mathlib.CategoryTheory.CommSq
import Mathlib.CategoryTheory.Limits.Opposites
import Mathlib.CategoryTheory.Limits.Shapes.Biproducts
imp... |
CategoryTheory\Limits\Shapes\Pullback\Cospan.lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks
import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
/-!
# Cospan & Span... |
CategoryTheory\Limits\Shapes\Pullback\HasPullback.lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel, Bhavik Mehta, Andrew Yang, Emily Riehl, Calle Sönne
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone
/-!
# HasPullback
`HasPullback ... |
CategoryTheory\Limits\Shapes\Pullback\Iso.lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
/-!
# The pullback of an isomorphism
This file provides some basic results about the pullback (and pu... |
CategoryTheory\Limits\Shapes\Pullback\Mono.lean | /-
Copyright (c) 2018 Scott Morrison. 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.Iso
/-!
# Pullbacks and monomorphisms
This file provides some results about interactions between pu... |
CategoryTheory\Limits\Shapes\Pullback\Pasting.lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Calle Sönne
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
/-!
# Pasting lemma
This file proves the pasting lemma for pullbacks. That is, given the... |
CategoryTheory\Limits\Shapes\Pullback\PullbackCone.lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel, Bhavik Mehta, Andrew Yang, Emily Riehl, Calle Sönne
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan
/-!
# PullbackCone
This file provide... |
CategoryTheory\Limits\Shapes\Pullback\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.Square
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
/-!
# Commutative squares that are pushout or pullback squares
In this file, ... |
CategoryTheory\Linear\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.Algebra.Algebra.Defs
import Mathlib.Algebra.Module.Equiv.Defs
import Mathlib.CategoryTheory.Preadditive.Basic
/-!
# Linear categories
An `R`-linear c... |
CategoryTheory\Linear\FunctorCategory.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.Preadditive.FunctorCategory
import Mathlib.CategoryTheory.Linear.Basic
/-!
# Linear structure on functor categories
If `C` and `D` are... |
CategoryTheory\Linear\LinearFunctor.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.Preadditive.AdditiveFunctor
import Mathlib.CategoryTheory.Linear.Basic
import Mathlib.Algebra.Module.LinearMap.Rat
/-!
# Linear Functor... |
CategoryTheory\Linear\Yoneda.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.Algebra.Category.ModuleCat.Basic
import Mathlib.CategoryTheory.Linear.Basic
import Mathlib.CategoryTheory.Preadditive.Yoneda.Basic
/-!
# The Yoneda em... |
CategoryTheory\Localization\Adjunction.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.CatCommSq
import Mathlib.CategoryTheory.Localization.Predicate
import Mathlib.CategoryTheory.Adjunction.FullyFaithful
/-!
# Localization of adjun... |
CategoryTheory\Localization\Bousfield.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.ClosedUnderIsomorphisms
import Mathlib.CategoryTheory.MorphismProperty.Composition
import Mathlib.CategoryTheory.Localization.Adjunction
/-!
# Bo... |
CategoryTheory\Localization\CalculusOfFractions.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.Localization.Opposite
/-!
# Calculus of fractions
Following the definitions by [Gabriel and Zisman][gabriel-zisman-1967],
given a morphism prope... |
CategoryTheory\Localization\Composition.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.Localization.LocalizerMorphism
/-!
# Composition of localization functors
Given two composable functors `L₁ : C₁ ⥤ C₂` and `L₂ : C₂ ⥤ C₃`, it is... |
CategoryTheory\Localization\Construction.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.MorphismProperty.Composition
import Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy
import Mathlib.CategoryTheory.Category.Quiv
/-!
# Const... |
CategoryTheory\Localization\Equivalence.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.Localization.Predicate
import Mathlib.CategoryTheory.CatCommSq
/-!
# Localization functors are preserved through equivalences
In `Localization/P... |
CategoryTheory\Localization\FiniteProducts.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.ConeCategory
import Mathlib.CategoryTheory.Limits.Preserves.Finite
import Mathlib.CategoryTheory.Localization.Adjunction
import Mathlib.Cat... |
CategoryTheory\Localization\HasLocalization.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.Localization.Predicate
/-! Morphism properties equipped with a localized category
If `C : Type u` is a category (with `[Category.{v} C]`), and
`... |
CategoryTheory\Localization\HomEquiv.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.Localization.LocalizerMorphism
import Mathlib.CategoryTheory.HomCongr
/-!
# Bijections between morphisms in two localized categories
Given two ... |
CategoryTheory\Localization\LocalizerMorphism.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.Localization.Equivalence
/-!
# Morphisms of localizers
A morphism of localizers consists of a functor `F : C₁ ⥤ C₂` between
two categories equip... |
CategoryTheory\Localization\Opposite.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.Localization.Predicate
/-!
# Localization of the opposite category
If a functor `L : C ⥤ D` is a localization functor for `W : MorphismProperty... |
CategoryTheory\Localization\Pi.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.Localization.Prod
import Mathlib.CategoryTheory.Localization.Equivalence
import Mathlib.Data.Fintype.Option
/-!
# Localization of product categor... |
CategoryTheory\Localization\Predicate.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.Localization.Construction
/-!
# Predicate for localized categories
In this file, a predicate `L.IsLocalization W` is introduced for a functor `... |
CategoryTheory\Localization\Prod.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.Currying
import Mathlib.CategoryTheory.Localization.Predicate
import Mathlib.CategoryTheory.MorphismProperty.Composition
/-!
# Localizati... |
CategoryTheory\Localization\Resolution.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.Localization.LocalizerMorphism
/-!
# Resolutions for a morphism of localizers
Given a morphism of localizers `Φ : LocalizerMorphism W₁ W₂` (i.e.... |
CategoryTheory\Localization\SmallHom.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.Localization.HomEquiv
import Mathlib.Logic.Small.Defs
/-!
# Shrinking morphisms in localized categories
Given a class of morphisms `W : Morphism... |
CategoryTheory\Localization\SmallShiftedHom.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.Localization.SmallHom
import Mathlib.CategoryTheory.Shift.ShiftedHom
import Mathlib.CategoryTheory.Shift.Localization
/-!
# Shrinking morphisms i... |
CategoryTheory\Localization\StructuredArrow.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.Localization.HomEquiv
import Mathlib.CategoryTheory.Localization.Opposite
import Mathlib.CategoryTheory.Comma.StructuredArrow
/-!
# Induction pri... |
CategoryTheory\Localization\Triangulated.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.Localization.CalculusOfFractions.ComposableArrows
import Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive
import Mathlib.Catego... |
CategoryTheory\Localization\CalculusOfFractions\ComposableArrows.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Andrew Yang
-/
import Mathlib.CategoryTheory.ComposableArrows
import Mathlib.CategoryTheory.Localization.CalculusOfFractions
/-! # Essential surjectivity of the functor induced ... |
CategoryTheory\Localization\CalculusOfFractions\Fractions.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.Localization.CalculusOfFractions
/-!
# Lemmas on fractions
Let `W : MorphismProperty C`, and objects `X` and `Y` in `C`. In this file,
we introd... |
CategoryTheory\Localization\CalculusOfFractions\Preadditive.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.Localization.CalculusOfFractions.Fractions
import Mathlib.CategoryTheory.Localization.HasLocalization
import Mathlib.CategoryTheory.Preadditive.Ad... |
CategoryTheory\Localization\DerivabilityStructure\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.Localization.Resolution
import Mathlib.CategoryTheory.GuitartExact.VerticalComposition
/-!
# Derivability structures
Let `Φ : LocalizerMorphism ... |
CategoryTheory\Localization\DerivabilityStructure\Constructor.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.Localization.DerivabilityStructure.Basic
/-!
# Constructor for derivability structures
In this file, we provide a constructor for right derivabi... |
CategoryTheory\Monad\Adjunction.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.Adjunction.Reflective
import Mathlib.CategoryTheory.Monad.Algebra
/-!
# Adjunctions and (co)monads
We develop the basic ... |
CategoryTheory\Monad\Algebra.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.Monad.Basic
import Mathlib.CategoryTheory.Adjunction.Basic
import Mathlib.CategoryTheory.Functor.EpiMono
/-!
# Eilenberg-... |
CategoryTheory\Monad\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, Bhavik Mehta, Adam Topaz
-/
import Mathlib.CategoryTheory.Functor.Category
import Mathlib.CategoryTheory.Functor.FullyFaithful
import Mathlib.CategoryTheory.Functor.Ref... |
CategoryTheory\Monad\Coequalizer.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.Reflexive
import Mathlib.CategoryTheory.Limits.Shapes.SplitCoequalizer
import Mathlib.CategoryTheory.Monad.Algebra
/-!
# Spec... |
CategoryTheory\Monad\Equalizer.lean | /-
Copyright (c) 2024 Jack McKoen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jack McKoen
-/
import Mathlib.CategoryTheory.Limits.Shapes.Reflexive
import Mathlib.CategoryTheory.Limits.Shapes.SplitEqualizer
import Mathlib.CategoryTheory.Monad.Algebra
/-!
# Special ... |
CategoryTheory\Monad\EquivMon.lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import Mathlib.CategoryTheory.Monad.Basic
import Mathlib.CategoryTheory.Monoidal.End
import Mathlib.CategoryTheory.Monoidal.Mon_
/-!
# The equivalence between `Monad C` and... |
CategoryTheory\Monad\Kleisli.lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Adjunction.Basic
import Mathlib.CategoryTheory.Monad.Basic
/-! # Kleisli category on a (co)monad
This file defines... |
CategoryTheory\Monad\Limits.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, Jack McKoen
-/
import Mathlib.CategoryTheory.Monad.Adjunction
import Mathlib.CategoryTheory.Adjunction.Limits
import Mathlib.CategoryTheory.Limits.Shapes.... |
CategoryTheory\Monad\Monadicity.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.Equalizers
import Mathlib.CategoryTheory.Limits.Shapes.Reflexive
import Mathlib.CategoryTheory.Monad.Coequalizer
imp... |
CategoryTheory\Monad\Products.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.Over
import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Monad.Algebra
/-!
# Algebras for the co... |
CategoryTheory\Monad\Types.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Monad.Basic
import Mathlib.CategoryTheory.Monad.Kleisli
import Mathlib.CategoryTheory.Category.KleisliCat
import Mathlib.C... |
CategoryTheory\Monoidal\Bimod.lean | /-
Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Oleksandr Manzyuk
-/
import Mathlib.CategoryTheory.Bicategory.Basic
import Mathlib.CategoryTheory.Monoidal.Mon_
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Eq... |
CategoryTheory\Monoidal\Bimon_.lean | /-
Copyright (c) 2024 Lean FRO LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.CategoryTheory.Monoidal.Comon_
/-!
# The category of bimonoids in a braided monoidal category.
We define bimonoids in a braided monoidal category `C`
as ... |
CategoryTheory\Monoidal\Category.lean | /-
Copyright (c) 2018 Michael Jendrusch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Scott Morrison, Bhavik Mehta, Jakob von Raumer
-/
import Mathlib.CategoryTheory.Functor.Trifunctor
import Mathlib.CategoryTheory.Products.Basic
/-!
# Monoidal ca... |
CategoryTheory\Monoidal\Center.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.Braided.Basic
import Mathlib.CategoryTheory.Functor.ReflectsIso
/-!
# Half braidings and the Drinfeld center of a monoidal cat... |
CategoryTheory\Monoidal\CoherenceLemmas.lean | /-
Copyright (c) 2018 Michael Jendrusch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Scott Morrison, Bhavik Mehta, Jakob von Raumer
-/
import Mathlib.Tactic.CategoryTheory.Coherence
/-!
# Lemmas which are consequences of monoidal coherence
These... |
CategoryTheory\Monoidal\CommMon_.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.Monoidal.Braided.Basic
import Mathlib.CategoryTheory.Monoidal.Mon_
/-!
# The category of commutative monoids in a braided monoidal cate... |
CategoryTheory\Monoidal\Comon_.lean | /-
Copyright (c) 2024 Lean FRO LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.CategoryTheory.Monoidal.Mon_
import Mathlib.CategoryTheory.Monoidal.Braided.Opposite
import Mathlib.CategoryTheory.Monoidal.Transport
import Mathlib.Catego... |
CategoryTheory\Monoidal\Conv.lean | /-
Copyright (c) 2024 Lean FRO LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.CategoryTheory.Monoidal.Comon_
/-!
# The convolution monoid.
When `M : Comon_ C` and `N : Mon_ C`, the morphisms `M.X ⟶ N.X` form a monoid (in Type).
-/
... |
CategoryTheory\Monoidal\Discrete.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.Algebra.Group.Hom.Defs
import Mathlib.CategoryTheory.DiscreteCategory
import Mathlib.CategoryTheory.Monoidal.NaturalTransformation
/-!
# Monoids as di... |
CategoryTheory\Monoidal\End.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Andrew Yang
-/
import Mathlib.CategoryTheory.Monoidal.Functor
/-!
# Endofunctors as a monoidal category.
We give the monoidal category structure on `C ⥤ C`,
and show ... |
CategoryTheory\Monoidal\Functor.lean | /-
Copyright (c) 2018 Michael Jendrusch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Scott Morrison, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Monoidal.Category
import Mathlib.CategoryTheory.Adjunction.FullyFaithful
import Mathlib.CategoryTheo... |
CategoryTheory\Monoidal\FunctorCategory.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.Monoidal.Braided.Basic
import Mathlib.CategoryTheory.Functor.Category
import Mathlib.CategoryTheory.Functor.Const
/-!
# Monoidal struct... |
CategoryTheory\Monoidal\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.Monoidal.Functor
import Mathlib.CategoryTheory.Functor.Functorial
/-!
# Unbundled lax monoidal functors
## Design considerations
The e... |
CategoryTheory\Monoidal\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
-/
import Mathlib.CategoryTheory.Monoidal.Functorial
import Mathlib.CategoryTheory.Monoidal.FunctorCategory
import Mathlib.CategoryTheory.Limits.HasLimits
/-!
# `lim : ... |
CategoryTheory\Monoidal\Linear.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.Linear.LinearFunctor
import Mathlib.CategoryTheory.Monoidal.Preadditive
/-!
# Linear monoidal categories
A monoidal category is `Monoi... |
CategoryTheory\Monoidal\Mod_.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.Monoidal.Mon_
/-!
# The category of module objects over a monoid object.
-/
universe v₁ v₂ u₁ u₂
open CategoryTheory MonoidalCategor... |
CategoryTheory\Monoidal\Mon_.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.Monoidal.Braided.Basic
import Mathlib.CategoryTheory.Monoidal.Discrete
import Mathlib.CategoryTheory.Monoidal.CoherenceLemmas
import Mat... |
CategoryTheory\Monoidal\NaturalTransformation.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.Adjunction.FullyFaithful
import Mathlib.CategoryTheory.Monoidal.Functor
import Mathlib.CategoryTheory.FullSubcategory
/-!
# Monoidal na... |
CategoryTheory\Monoidal\OfHasFiniteProducts.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Simon Hudon
-/
import Mathlib.CategoryTheory.Monoidal.Braided.Basic
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts
import Mathlib.CategoryTheory.L... |
CategoryTheory\Monoidal\Opposite.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.Tactic.CategoryTheory.Coherence
/-!
# Monoidal opposites
We write `Cᵐᵒᵖ` for the monoidal opposite of a monoidal category `C`.
-/
universe v₁ v₂ u₁... |
CategoryTheory\Monoidal\Preadditive.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.Preadditive.AdditiveFunctor
import Mathlib.CategoryTheory.Monoidal.Functor
/-!
# Preadditive monoidal categories
A monoidal category i... |
CategoryTheory\Monoidal\Skeleton.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.Monoidal.Braided.Basic
import Mathlib.CategoryTheory.Monoidal.Transport
import Mathlib.CategoryTheory.Skeletal
/-!
# The monoid on the skel... |
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