path stringlengths 11 71 | content stringlengths 75 124k |
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CategoryTheory\Monoidal\Subcategory.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.Monoidal.Braided.Basic
import Mathlib.CategoryTheory.Monoidal.Linear
import Mathlib.CategoryTheory.Monoidal.Transport
import Mathlib.C... |
CategoryTheory\Monoidal\Tor.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.Abelian.LeftDerived
import Mathlib.CategoryTheory.Monoidal.Preadditive
/-!
# Tor, the left-derived functor of tensor product
We define... |
CategoryTheory\Monoidal\Transport.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.NaturalTransformation
/-!
# Transport a monoidal structure along an equivalence.
When `C` and `D` are equivalent as categorie... |
CategoryTheory\Monoidal\Braided\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
-/
import Mathlib.CategoryTheory.Monoidal.Discrete
import Mathlib.CategoryTheory.Monoidal.NaturalTransformation
import Mathlib.CategoryTheory.Monoidal.Opposite
import Ma... |
CategoryTheory\Monoidal\Braided\Opposite.lean | /-
Copyright (c) 2024 Lean FRO LLC. 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.Opposite
/-!
# If `C` is braided, so is `Cᵒᵖ`.
Todo: we should also do `Cᵐ... |
CategoryTheory\Monoidal\Cartesian\Comon_.lean | /-
Copyright (c) 2023 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_
import Mathlib.CategoryTheory.Monoidal.OfHasFiniteProducts
/-!
# Comonoid objects in a cartesian monoidal category.
The ca... |
CategoryTheory\Monoidal\Free\Basic.lean | /-
Copyright (c) 2021 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Monoidal.Functor
/-!
# The free monoidal category over a type
Given a type `C`, the free monoidal category over `C` has as objects forma... |
CategoryTheory\Monoidal\Free\Coherence.lean | /-
Copyright (c) 2021 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Monoidal.Free.Basic
import Mathlib.CategoryTheory.DiscreteCategory
/-!
# The monoidal coherence theorem
In this file, we prove the monoi... |
CategoryTheory\Monoidal\Internal\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.CommMon_
import Mathlib.CategoryTheory.Monoidal.Comon_
import Mathlib.CategoryTheory.Monoidal.FunctorCategory
/-!
# `Mon_ (C ⥤... |
CategoryTheory\Monoidal\Internal\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.Internal.FunctorCategory
import Mathlib.CategoryTheory.Monoidal.Limits
import Mathlib.CategoryTheory.Limits.Preserves.Basic
/-... |
CategoryTheory\Monoidal\Internal\Module.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.Category.ModuleCat.Monoidal.Basic
import Mathlib.Algebra.Category.AlgebraCat.Basic
import Mathlib.CategoryTheory.Monoidal.Mon_
/-!
# `Mon_ (Mo... |
CategoryTheory\Monoidal\Internal\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.Algebra.Category.MonCat.Basic
import Mathlib.CategoryTheory.Monoidal.CommMon_
import Mathlib.CategoryTheory.Monoidal.Types.Symmetric
/-!
# `Mon_ (Type... |
CategoryTheory\Monoidal\OfChosenFiniteProducts\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, Simon Hudon
-/
import Mathlib.CategoryTheory.Monoidal.Category
import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
import Mathlib.CategoryTheory.PEmpty
/-!
# Th... |
CategoryTheory\Monoidal\OfChosenFiniteProducts\Symmetric.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.Monoidal.OfChosenFiniteProducts.Basic
/-!
# The symmetric monoidal st... |
CategoryTheory\Monoidal\Rigid\Basic.lean | /-
Copyright (c) 2021 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
import Mathlib.Tactic.CategoryTheory.Coherence
import Mathlib.CategoryTheory.Closed.Monoidal
import Mathlib.Tactic.ApplyFun
/-!
# Rigid (autonomous) monoidal cat... |
CategoryTheory\Monoidal\Rigid\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.Monoidal.Rigid.Basic
import Mathlib.CategoryTheory.Monoidal.FunctorCategory
/-!
# Functors from a groupoid into a right/left rigid cate... |
CategoryTheory\Monoidal\Rigid\OfEquivalence.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.Monoidal.Rigid.Basic
/-!
# Transport rigid structures over a monoidal equivalence.
-/
noncomputable section
namespace CategoryTheory... |
CategoryTheory\Monoidal\Types\Basic.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
-/
import Mathlib.CategoryTheory.Monoidal.Functor
import Mathlib.CategoryTheory.ChosenFiniteProducts
import Mathlib.CategoryTheory.Limits.Shapes.Ty... |
CategoryTheory\Monoidal\Types\Coyoneda.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
-/
import Mathlib.CategoryTheory.Monoidal.Types.Basic
import Mathlib.CategoryTheory.Monoidal.CoherenceLemmas
/-!
# `(𝟙_ C ⟶ -)` is a lax monoidal... |
CategoryTheory\Monoidal\Types\Symmetric.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
-/
import Mathlib.CategoryTheory.Monoidal.OfChosenFiniteProducts.Symmetric
import Mathlib.CategoryTheory.Monoidal.Types.Basic
/-!
# The category o... |
CategoryTheory\MorphismProperty\Basic.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.Comma.Arrow
import Mathlib.CategoryTheory.Pi.Basic
import Mathlib.Order.CompleteBooleanAlgebra
/-!
# Properties of morphisms
We provide the ... |
CategoryTheory\MorphismProperty\Composition.lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Joël Riou
-/
import Mathlib.CategoryTheory.MorphismProperty.Basic
/-!
# Compatibilities of properties of morphisms with respect to composition
Given `P : MorphismProperty C... |
CategoryTheory\MorphismProperty\Concrete.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.ConcreteCategory.Basic
import Mathlib.CategoryTheory.MorphismProperty.Composition
import Mathlib.CategoryTheory.MorphismProperty.Factorization... |
CategoryTheory\MorphismProperty\Factorization.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.MorphismProperty.Basic
/-!
# The factorization axiom
In this file, we introduce a type-class `HasFactorization W₁ W₂`, which, given
two classes ... |
CategoryTheory\MorphismProperty\IsInvertedBy.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.Functor.ReflectsIso
import Mathlib.CategoryTheory.MorphismProperty.Basic
/-!
# Morphism properties that are inverted by a functor
In this file, ... |
CategoryTheory\MorphismProperty\Limits.lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Joël Riou
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Diagonal
import Mathlib.CategoryTheory.MorphismProperty.C... |
CategoryTheory\Pi\Basic.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Scott Morrison
-/
import Mathlib.CategoryTheory.EqToHom
import Mathlib.CategoryTheory.NatIso
import Mathlib.CategoryTheory.Products.Basic
import Batteries.Data.Sum.Basic
... |
CategoryTheory\Preadditive\AdditiveFunctor.lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Scott Morrison
-/
import Mathlib.CategoryTheory.Limits.ExactFunctor
import Mathlib.CategoryTheory.Limits.Preserves.Finite
import Mathlib.CategoryTheory.Preadditive.Biproducts
i... |
CategoryTheory\Preadditive\Basic.lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Jakob von Raumer
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Algebra.Group.Hom.Defs
import Mathlib.Algebra.Module.Defs
import Mathlib.CategoryTheor... |
CategoryTheory\Preadditive\Biproducts.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.Ext
import Mathlib.CategoryTheory.Limits.Shapes.Biproducts
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts
import Ma... |
CategoryTheory\Preadditive\EilenbergMoore.lean | /-
Copyright (c) 2022 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
import Mathlib.CategoryTheory.Preadditive.Basic
import Mathlib.CategoryTheory.Monad.Algebra
import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
/-!
# P... |
CategoryTheory\Preadditive\EndoFunctor.lean | /-
Copyright (c) 2022 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
import Mathlib.CategoryTheory.Preadditive.Basic
import Mathlib.CategoryTheory.Endofunctor.Algebra
import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
/... |
CategoryTheory\Preadditive\FunctorCategory.lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.CategoryTheory.Preadditive.Basic
/-!
# Preadditive structure on functor categories
If `C` and `D` are categories and `D` is preadditive,
then `C ⥤ D`... |
CategoryTheory\Preadditive\Generator.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.Generator
import Mathlib.CategoryTheory.Preadditive.Yoneda.Basic
/-!
# Separators in preadditive categories
This file contains character... |
CategoryTheory\Preadditive\HomOrthogonal.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.Basic
import Mathlib.CategoryTheory.Preadditive.Biproducts
import Mathlib.LinearAlgebra.Matrix.InvariantBasisNumber
import Mathli... |
CategoryTheory\Preadditive\Injective.lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Kevin Buzzard
-/
import Mathlib.CategoryTheory.Preadditive.Projective
/-!
# Injective objects and categories with enough injectives
An object `J` is injective iff every m... |
CategoryTheory\Preadditive\InjectiveResolution.lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Scott Morrison, Joël Riou
-/
import Mathlib.Algebra.Homology.QuasiIso
import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
import Mathlib.Algebra.Homology.Single... |
CategoryTheory\Preadditive\LeftExact.lean | /-
Copyright (c) 2022 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Jakob von Raumer
-/
import Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels
imp... |
CategoryTheory\Preadditive\Mat.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.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Pi
import Mathlib.CategoryTheory.Limits.Shapes.Biproducts
import Mathlib.Category... |
CategoryTheory\Preadditive\OfBiproducts.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.GroupTheory.EckmannHilton
import Mathlib.Tactic.CategoryTheory.Reassoc
/-!
# Constructing a semiad... |
CategoryTheory\Preadditive\Opposite.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Adam Topaz, Johan Commelin, Joël Riou
-/
import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
import Mathlib.Logic.Equiv.TransferInstance
/-!
# If `C` is preaddit... |
CategoryTheory\Preadditive\Projective.lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
-/
import Mathlib.CategoryTheory.Adjunction.FullyFaithful
import Mathlib.CategoryTheory.Adjunction.Limits
import Mathlib.CategoryTheory.Limits.Construction... |
CategoryTheory\Preadditive\ProjectiveResolution.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Joël Riou
-/
import Mathlib.Algebra.Homology.QuasiIso
import Mathlib.Algebra.Homology.SingleHomology
/-!
# Projective resolutions
A projective resolution `P : Project... |
CategoryTheory\Preadditive\Schur.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
-/
import Mathlib.Algebra.Group.Ext
import Mathlib.CategoryTheory.Simple
import Mathlib.CategoryTheory.Linear.Basic
import Mathlib.CategoryTheory.Endomorp... |
CategoryTheory\Preadditive\SingleObj.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.Basic
import Mathlib.CategoryTheory.SingleObj
/-!
# `SingleObj α` is preadditive when `α` is a ring.
-/
namespace Catego... |
CategoryTheory\Preadditive\Yoneda\Basic.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.Preadditive.Opposite
import Mathlib.Algebra.Category.ModuleCat.Basic
import Mathlib.Algebra.Category.Grp.Preadditive
/-!
# The Yoneda emb... |
CategoryTheory\Preadditive\Yoneda\Injective.lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
-/
import Mathlib.CategoryTheory.Preadditive.Yoneda.Basic
import Mathlib.CategoryTheory.Preadditive.Injective
import Mathlib.Algebra.Category.Grp.EpiMono
i... |
CategoryTheory\Preadditive\Yoneda\Limits.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.Preadditive.Yoneda.Basic
import Mathlib.Algebra.Category.ModuleCat.Abelian
import Mathlib.CategoryTheory.Limits.Yoneda
/-!
# The Yoneda e... |
CategoryTheory\Preadditive\Yoneda\Projective.lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
-/
import Mathlib.CategoryTheory.Preadditive.Yoneda.Basic
import Mathlib.CategoryTheory.Preadditive.Projective
import Mathlib.Algebra.Category.Grp.EpiMono
... |
CategoryTheory\Products\Associator.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
-/
import Mathlib.CategoryTheory.Products.Basic
/-!
The associator functor `((C × D) × E) ⥤ (C × (D × E))` and its inverse form an equivalence.
-/
uni... |
CategoryTheory\Products\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
-/
import Mathlib.CategoryTheory.EqToHom
import Mathlib.CategoryTheory.Functor.Const
import Mathlib.CategoryTheory.Opposites
import Mathlib.Data.Prod.Bas... |
CategoryTheory\Products\Bifunctor.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
-/
import Mathlib.CategoryTheory.Products.Basic
/-!
# Lemmas about functors out of product categories.
-/
open CategoryTheory
namespace CategoryTheor... |
CategoryTheory\Products\Unitor.lean | /-
Copyright (c) 2024 Shanghe Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shanghe Chen
-/
import Mathlib.CategoryTheory.Products.Basic
import Mathlib.CategoryTheory.DiscreteCategory
/-!
# The left/right unitor equivalences `1 × C ≌ C` and `C × 1 ≌ C`.
-/
uni... |
CategoryTheory\Quotient\Linear.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.Quotient
import Mathlib.CategoryTheory.Linear.LinearFunctor
/-!
# The quotient category is linear
If `r : HomRel C` is a congruence on a preaddi... |
CategoryTheory\Quotient\Preadditive.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.Quotient
import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
/-!
# The quotient category is preadditive
If an equivalence relation `r : Ho... |
CategoryTheory\Shift\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, Johan Commelin, Andrew Yang
-/
import Mathlib.Algebra.Group.Basic
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero
import Mathlib.CategoryTheory.Monoidal.End
... |
CategoryTheory\Shift\CommShift.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.Shift.Basic
/-!
# Functors which commute with shifts
Let `C` and `D` be two categories equipped with shifts by an additive monoid `A`. In this ... |
CategoryTheory\Shift\Induced.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.Shift.CommShift
/-!
# Shift induced from a category to another
In this file, we introduce a sufficient condition on a functor
`F : C ⥤ D` so tha... |
CategoryTheory\Shift\InducedShiftSequence.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.Shift.CommShift
import Mathlib.CategoryTheory.Shift.ShiftSequence
/-! # Induced shift sequences
When `G : C ⥤ A` is a functor from a category eq... |
CategoryTheory\Shift\Localization.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.Shift.Induced
import Mathlib.CategoryTheory.Localization.HasLocalization
import Mathlib.CategoryTheory.Localization.LocalizerMorphism
/-!
# The s... |
CategoryTheory\Shift\Opposite.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.Shift.Basic
import Mathlib.CategoryTheory.Preadditive.Opposite
/-!
# The (naive) shift on the opposite category
If `C` is a category equipped wi... |
CategoryTheory\Shift\Predicate.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.Shift.Basic
/-!
# Predicates on categories equipped with shift
Given a predicate `P : C → ... |
CategoryTheory\Shift\Pullback.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.Shift.Basic
import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
/-!
# The pullback of a shift by a monoid morphism
Given a shift by a mono... |
CategoryTheory\Shift\Quotient.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.Shift.CommShift
import Mathlib.CategoryTheory.Shift.Induced
import Mathlib.CategoryTheory.Quotient
/-!
# The shift on a quotient category
Let `C... |
CategoryTheory\Shift\ShiftedHom.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.Shift.CommShift
import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
/-! Shifted morphisms
Given a category `C` endowed with a shift by an ... |
CategoryTheory\Shift\ShiftSequence.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.Shift.Basic
import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
/-! Sequences of functors from a category equipped with a shift
Let `F : C... |
CategoryTheory\Shift\SingleFunctors.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.Shift.CommShift
/-!
# Functors from a category to a category with a shift
Given a category `C`, and a category `D` equipped with a shift by a mo... |
CategoryTheory\Sigma\Basic.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.Whiskering
import Mathlib.CategoryTheory.Functor.FullyFaithful
import Mathlib.CategoryTheory.NatIso
/-!
# Disjoint union of categories
We ... |
CategoryTheory\Sites\Abelian.lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Jujian Zhang
-/
import Mathlib.CategoryTheory.Abelian.FunctorCategory
import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
import Mathlib.CategoryTheory.Abelian.Transfer... |
CategoryTheory\Sites\Adjunction.lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Joël Riou
-/
import Mathlib.CategoryTheory.Adjunction.Whiskering
import Mathlib.CategoryTheory.Sites.PreservesSheafification
/-!
In this file, we show that an adjunction `G ⊣... |
CategoryTheory\Sites\Canonical.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.Sites.Sheaf
/-!
# The canonical topology on a category
We define the finest (largest) Grothendieck topology for which a given presheaf `P`... |
CategoryTheory\Sites\Closed.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.Sites.SheafOfTypes
import Mathlib.Order.Closure
/-!
# Closed sieves
A natural closure operator on sieves is a closure operator on `Sieve X... |
CategoryTheory\Sites\CompatiblePlus.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.Sites.Whiskering
import Mathlib.CategoryTheory.Sites.Plus
/-!
In this file, we prove that the plus functor is compatible with functors which
p... |
CategoryTheory\Sites\CompatibleSheafification.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.Sites.CompatiblePlus
import Mathlib.CategoryTheory.Sites.ConcreteSheafification
/-!
In this file, we prove that sheafification is compatible w... |
CategoryTheory\Sites\ConcreteSheafification.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.Sites.Plus
import Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory
/-!
# Sheafification
We construct the sheafification of a presheaf ov... |
CategoryTheory\Sites\ConstantSheaf.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.Sites.Sheafification
/-!
# The constant sheaf
We define the constant sheaf functor (the sheafification of the constant presheaf)
... |
CategoryTheory\Sites\Continuous.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.Sites.IsSheafOneHypercover
/-!
# Continuous functors between sites.
We define the notion of continuous functor between sites: these... |
CategoryTheory\Sites\Coverage.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.Sites.Sheaf
/-!
# Coverages
A coverage `K` on a category `C` is a set of presieves associated to every object `X : C`,
called "covering pres... |
CategoryTheory\Sites\CoverLifting.lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Joël Riou
-/
import Mathlib.CategoryTheory.Adjunction.Restrict
import Mathlib.CategoryTheory.Functor.KanExtension.Adjunction
import Mathlib.CategoryTheory.Sites.Continuous
im... |
CategoryTheory\Sites\CoverPreserving.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.Functor.Flat
import Mathlib.CategoryTheory.Sites.Continuous
import Mathlib.Tactic.ApplyFun
/-!
# Cover-preserving functors between sites.
In ... |
CategoryTheory\Sites\CoversTop.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.Sites.Sheaf
/-! Objects which cover the terminal object
In this file, given a site `(C, J)`, we introduce the notion of a family
of objects `Y :... |
CategoryTheory\Sites\DenseSubsite.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.Sites.Sheaf
import Mathlib.CategoryTheory.Sites.CoverLifting
import Mathlib.CategoryTheory.Sites.CoverPreserving
import Mathlib.CategoryTheory... |
CategoryTheory\Sites\Discrete.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.Adjunction.FullyFaithful
import Mathlib.CategoryTheory.Sites.ConstantSheaf
import Mathlib.CategoryTheory.Sites.DenseSubsite
import M... |
CategoryTheory\Sites\EffectiveEpimorphic.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.Sites.Sieves
import Mathlib.CategoryTheory.EffectiveEpi.Basic
/-!
# Effective epimorphic sieves
We define the notion of effective epimorphic (... |
CategoryTheory\Sites\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.MorphismProperty.Concrete
import Mathlib.CategoryTheory.Sites.LocallyBijective
/-!
# Morphisms of sheaves factor as a locally surjective followed... |
CategoryTheory\Sites\EqualizerSheafCondition.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.Sites.IsSheafFor
import Mathlib.CategoryTheory.Limits.Shapes.Types
import Mathlib.Tactic.ApplyFun
/-!
# The equalizer diagram sheaf conditi... |
CategoryTheory\Sites\Equivalence.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.Sites.InducedTopology
import Mathlib.CategoryTheory.Sites.LocallyBijective
import Mathlib.CategoryTheory.Sites.PreservesLocallyBijec... |
CategoryTheory\Sites\Grothendieck.lean | /-
Copyright (c) 2020 Bhavik Mehta, E. W. Ayers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, E. W. Ayers
-/
import Mathlib.CategoryTheory.Sites.Sieves
import Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
import Mathlib.CategoryTheory.Category.Pre... |
CategoryTheory\Sites\InducedTopology.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.Sites.DenseSubsite
/-!
# Induced Topology
We say that a functor `G : C ⥤ (D, K)` is locally dense if for each covering sieve `T` in `D` of
s... |
CategoryTheory\Sites\IsSheafFor.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.Sites.Sieves
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono
/-!
# The sheaf condition for a presieve
We define what it means fo... |
CategoryTheory\Sites\IsSheafOneHypercover.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.Sites.OneHypercover
/-!
# Characterization of sheaves using 1-hypercovers
In this file, given a Grothendieck topology `J` on a category `C`,
we ... |
CategoryTheory\Sites\LeftExact.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.Sites.Limits
import Mathlib.CategoryTheory.Limits.FilteredColimitCommutesFiniteLimit
import Mathlib.CategoryTheory.Adhesive
import Mathlib.Categ... |
CategoryTheory\Sites\Limits.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.Creates
import Mathlib.CategoryTheory.Sites.Sheafification
import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts
/-!
# Limits and ... |
CategoryTheory\Sites\Localization.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.Bousfield
import Mathlib.CategoryTheory.Sites.Sheafification
/-!
# The sheaf category as a localized category
In this file, it is s... |
CategoryTheory\Sites\LocallyBijective.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.Sites.LocallySurjective
import Mathlib.CategoryTheory.Sites.Localization
/-!
# Locally bijective morphisms of presheaves
Let `C` a be category e... |
CategoryTheory\Sites\LocallyFullyFaithful.lean | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.CategoryTheory.Sites.LocallySurjective
/-!
# Locally fully faithful functors into sites
## Main results
- `CategoryTheory.Functor.IsLocallyFull`:
A func... |
CategoryTheory\Sites\LocallyInjective.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.Sites.LeftExact
import Mathlib.CategoryTheory.Sites.PreservesSheafification
import Mathlib.CategoryTheory.Sites.Subsheaf
import Mathlib.CategoryTh... |
CategoryTheory\Sites\LocallySurjective.lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Joël Riou
-/
import Mathlib.CategoryTheory.Sites.Subsheaf
import Mathlib.CategoryTheory.Sites.CompatibleSheafification
import Mathlib.CategoryTheory.Sites.LocallyInjective
/-... |
CategoryTheory\Sites\MayerVietorisSquare.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.Shapes.Types
import Mathlib.CategoryTheory.Sites.Sheafification
/-!
# Mayer-Vi... |
CategoryTheory\Sites\OneHypercover.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.Sites.Sheaf
/-!
# 1-hypercovers
Given a Grothendieck topology `J` on a category `C`, we define the type of
`1`-hypercovers of an object `S : C`.... |
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