path stringlengths 11 71 | content stringlengths 75 124k |
|---|---|
Analysis\SpecialFunctions\Trigonometric\Angle.lean | /-
Copyright (c) 2019 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne
-/
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
import Mathlib.Analysis.Normed.Group.AddCircle
import Mathlib.Algebra.CharZero.Quotient
import Mathlib.Topology... |
Analysis\SpecialFunctions\Trigonometric\Arctan.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex
/-!
# The `arctan` function.
Inequalit... |
Analysis\SpecialFunctions\Trigonometric\ArctanDeriv.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan
import Mathlib.Analysis.SpecialFunctions.... |
Analysis\SpecialFunctions\Trigonometric\Basic.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
import Mathlib.Analysis.SpecialFunctions.Exp
import Mathlib.Tactic.Positivity.Core
import Mathlib.Algeb... |
Analysis\SpecialFunctions\Trigonometric\Bounds.lean | /-
Copyright (c) 2022 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler, Yaël Dillies
-/
import Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv
/-!
# Polynomial bounds for trigonometric functions
## Main statements
This file c... |
Analysis\SpecialFunctions\Trigonometric\Chebyshev.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.Polynomial.AlgebraMap
import Mathlib.Data.Complex.Exponential
import Mathlib.Data.Complex.Module
import Mathlib.RingTheory.Polynomial.Chebyshev... |
Analysis\SpecialFunctions\Trigonometric\Complex.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
import Mathlib.Algebra.QuadraticDiscriminant
import Mathlib.Analysis.Convex.SpecificFunctions.Deriv
imp... |
Analysis\SpecialFunctions\Trigonometric\ComplexDeriv.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex
/-!
# Complex trigonometric functions
... |
Analysis\SpecialFunctions\Trigonometric\Cotangent.lean | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
import Mathlib.Analysis.Complex.UpperHalfPlane.Exp
/-!
# Cotangent
This file contains lemmas about the cotangent function, including useful series expansions.
-/
o... |
Analysis\SpecialFunctions\Trigonometric\Deriv.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
import Mathlib.Order.Monotone.Odd
import Mathlib.Analysis.Calculus.LogDeriv
import Mathlib.Analysis.Spe... |
Analysis\SpecialFunctions\Trigonometric\EulerSineProd.lean | /-
Copyright (c) 2023 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
import Mathlib.Analysis.SpecialFunctions.Integrals
import Mathlib.MeasureTheory.Integral.PeakFunction
/-! # Euler's infinite product for the sine function
This file... |
Analysis\SpecialFunctions\Trigonometric\Inverse.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
import Mathlib.Topology.Order.ProjIcc
/-!... |
Analysis\SpecialFunctions\Trigonometric\InverseDeriv.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse
import Mathlib.Analysis.SpecialFunctions... |
Analysis\SpecialFunctions\Trigonometric\Series.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Yaël Dillies
-/
import Mathlib.Analysis.SpecialFunctions.Exponential
/-!
# Trigonometric functions as sums of infinite series
In this file we express trigonometric function... |
Analysis\SpecificLimits\Basic.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Johannes Hölzl, Yury G. Kudryashov, Patrick Massot
-/
import Mathlib.Algebra.GeomSum
import Mathlib.Order.Filter.Archimedean
import Mathlib.Order.Iterate
import Math... |
Analysis\SpecificLimits\FloorPow.lean | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Analysis.SpecificLimits.Basic
import Mathlib.Analysis.SpecialFunctions.Pow.Real
/-!
# Results on discretized exponentials
We state several auxi... |
Analysis\SpecificLimits\Normed.lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Sébastien Gouëzel, Yury G. Kudryashov, Dylan MacKenzie, Patrick Massot
-/
import Mathlib.Algebra.BigOperators.Module
import Mathlib.Algebra.Order.Field.Basic
impor... |
Analysis\SpecificLimits\RCLike.lean | /-
Copyright (c) 2023 Xavier Généreux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Généreux, Patrick Massot
-/
import Mathlib.Analysis.SpecificLimits.Basic
import Mathlib.Analysis.RCLike.Basic
/-!
# A collection of specific limit computations for `RCLike`
-... |
Analysis\VonNeumannAlgebra\Basic.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.Analysis.Normed.Module.Dual
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.InnerProductSpace.Adjoint
/-!
# Von Neumann algebras
We giv... |
CategoryTheory\Action.lean | /-
Copyright (c) 2020 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import Mathlib.CategoryTheory.Elements
import Mathlib.CategoryTheory.IsConnected
import Mathlib.CategoryTheory.SingleObj
import Mathlib.GroupTheory.GroupAction.Quotient
impor... |
CategoryTheory\Adhesive.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.Extensive
import Mathlib.CategoryTheory.Limits.Shapes.KernelPair
import Mathlib.CategoryTheory.Limits.Constructions.EpiMono
/-!
# Adhesive c... |
CategoryTheory\Balanced.lean | /-
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.EpiMono
/-!
# Balanced categories
A category is called balanced if any morphism that is both monic and epic is an isomorphism.
Balanced... |
CategoryTheory\CatCommSq.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.Equivalence
/-!
# 2-commutative squares of functors
Similarly as `CommSq.lean` defines the notion of commutative squares,
this file introduces t... |
CategoryTheory\ChosenFiniteProducts.lean | /-
Copyright (c) 2024 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import Mathlib.CategoryTheory.Monoidal.OfChosenFiniteProducts.Symmetric
import Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts
/-!
# Categories wi... |
CategoryTheory\ClosedUnderIsomorphisms.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.Iso
import Mathlib.Order.Basic
/-! # Predicates on objects which are closed under isomorphisms
This file introduces the type class `ClosedUnderI... |
CategoryTheory\CofilteredSystem.lean | /-
Copyright (c) 2022 Kyle Miller, Adam Topaz, Rémi Bottinelli, Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Adam Topaz, Rémi Bottinelli, Junyan Xu
-/
import Mathlib.CategoryTheory.Filtered.Basic
import Mathlib.Data.Set.Finite
import Mathlib.D... |
CategoryTheory\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
-/
import Mathlib.CategoryTheory.Comma.Arrow
/-!
# Commutative squares
This file provide an API for commutative squares in categories.
If `top`, `left`, `ri... |
CategoryTheory\ComposableArrows.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.Category.Preorder
import Mathlib.CategoryTheory.EqToHom
import Mathlib.CategoryTheory.Functor.Const
import Mathlib.Order.Fin.Basic
import Mathlib.... |
CategoryTheory\Conj.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.Group.Units.Equiv
import Mathlib.CategoryTheory.Endomorphism
import Mathlib.CategoryTheory.HomCongr
/-!
# Conjugate morphisms by isomorphism... |
CategoryTheory\ConnectedComponents.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.Data.List.Chain
import Mathlib.CategoryTheory.IsConnected
import Mathlib.CategoryTheory.Sigma.Basic
import Mathlib.CategoryTheory.FullSubcategory
/-!
# Co... |
CategoryTheory\Core.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.Control.EquivFunctor
import Mathlib.CategoryTheory.Groupoid
import Mathlib.CategoryTheory.Whiskering
import Mathlib.CategoryTheory.Types
/-!
# The cor... |
CategoryTheory\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.Data.Countable.Small
import Mathlib.CategoryTheory.EssentiallySmall
import Mathlib.CategoryTheory.FinCategory.Basic
import Mathlib.Data.Fintype.Car... |
CategoryTheory\DifferentialObject.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.Basic
import Mathlib.Data.Int.Cast.Defs
import Mathlib.CategoryTheory.Shift.Basic
import Mathlib.CategoryTheory.ConcreteCategory.Basic
/... |
CategoryTheory\DiscreteCategory.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.EqToHom
import Mathlib.CategoryTheory.Pi.Basic
import Mathlib.Data.ULift
/-!
# Discrete categories
W... |
CategoryTheory\Elements.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.Comma.StructuredArrow
import Mathlib.CategoryTheory.Groupoid
import Mathlib.CategoryTheory.PUnit
/-!
# The category of elements
This f... |
CategoryTheory\Elementwise.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.Tactic.CategoryTheory.Elementwise
import Mathlib.CategoryTheory.ConcreteCategory.Basic
/-!
# Use the `elementwise` attribute to create applied version... |
CategoryTheory\Endomorphism.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Scott Morrison, Simon Hudon
-/
import Mathlib.Algebra.Group.Action.Defs
import Mathlib.Algebra.Group.Equiv.Basic
import Mathlib.Algebra.Group.Units
import Mathlib.Alg... |
CategoryTheory\EpiMono.lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Scott Morrison
-/
import Mathlib.CategoryTheory.Opposites
import Mathlib.CategoryTheory.Groupoid
/-!
# Facts about epimorphisms and monomorphisms.
The definitions of `Epi` ... |
CategoryTheory\EqToHom.lean | /-
Copyright (c) 2018 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Scott Morrison
-/
import Mathlib.CategoryTheory.Opposites
/-!
# Morphisms from equations between objects.
When working categorically, sometimes one encounters an equation `... |
CategoryTheory\Equivalence.lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baumann, Stephen Morgan, Scott Morrison, Floris van Doorn
-/
import Mathlib.CategoryTheory.Functor.FullyFaithful
import Mathlib.CategoryTheory.FullSubcategory
import Mathlib.Catego... |
CategoryTheory\EssentialImage.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.NatIso
import Mathlib.CategoryTheory.FullSubcategory
/-!
# Essential image of a functor
The essential image `essImage` of a functor consis... |
CategoryTheory\EssentiallySmall.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.Category.ULift
import Mathlib.CategoryTheory.Skeletal
import Mathlib.Logic.UnivLE
import Mathlib.Logic.Small.Basic
/-!
# Essentially sm... |
CategoryTheory\Extensive.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.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.StrictInitial
import Mathlib.CategoryTheory.Limits.Shapes.Types
impo... |
CategoryTheory\FintypeCat.lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Adam Topaz
-/
import Mathlib.CategoryTheory.ConcreteCategory.Basic
import Mathlib.CategoryTheory.FullSubcategory
import Mathlib.CategoryTheory.Skeletal
import Mathlib.Data.Fi... |
CategoryTheory\FullSubcategory.lean | /-
Copyright (c) 2017 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.Functor.FullyFaithful
/-!
# Induced categories and full subcategories
Given a category `D` and a function `F : C → D `fro... |
CategoryTheory\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.Balanced
import Mathlib.CategoryTheory.Limits.EssentiallySmall
import Mathlib.CategoryTheory.Limits.Opposites
import Mathlib.CategoryTheor... |
CategoryTheory\GlueData.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.Tactic.CategoryTheory.Elementwise
import Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
import Mathlib.CategoryTheory.Limits.Constructions.EpiMono
impor... |
CategoryTheory\GradedObject.lean | /-
Copyright (c) 2020 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.Group.Int
import Mathlib.CategoryTheory.ConcreteCategory.Basic
import Mathlib.CategoryTheory.Shift.Basic
import Mathlib.Data.Set.Sub... |
CategoryTheory\Grothendieck.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Sina Hazratpour
-/
import Mathlib.CategoryTheory.Category.Cat
import Mathlib.CategoryTheory.Elements
import Mathlib.CategoryTheory.Comma.Over
/-!
# The Grothendieck co... |
CategoryTheory\Groupoid.lean | /-
Copyright (c) 2018 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Scott Morrison, David Wärn
-/
import Mathlib.CategoryTheory.FullSubcategory
import Mathlib.CategoryTheory.Products.Basic
import Mathlib.CategoryTheory.Pi.Basic
import Mathlib... |
CategoryTheory\HomCongr.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.CategoryTheory.Iso
/-!
# Conjugate morphisms by isomorphisms
We define
`CategoryTheory.Iso.homCongr : (X ≅ X₁) → (Y ≅ Y₁) → (X ⟶ Y) ≃ (X₁ ⟶ Y₁)`,
c... |
CategoryTheory\IsConnected.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.Data.List.Chain
import Mathlib.CategoryTheory.PUnit
import Mathlib.CategoryTheory.Groupoid
import Mathlib.CategoryTheory.Category.ULift
... |
CategoryTheory\Iso.lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baumann, Stephen Morgan, Scott Morrison, Floris van Doorn
-/
import Mathlib.Tactic.CategoryTheory.Reassoc
/-!
# Isomorphisms
This file defines isomorphisms between objects of a c... |
CategoryTheory\IsomorphismClasses.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.CategoryTheory.Category.Cat
import Mathlib.CategoryTheory.Groupoid
import Mathlib.CategoryTheory.Types
/-!
# Objects of a category up to an isomorph... |
CategoryTheory\NatIso.lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baumann, Stephen Morgan, Scott Morrison, Floris van Doorn
-/
import Mathlib.CategoryTheory.Functor.Category
import Mathlib.CategoryTheory.Iso
/-!
# Natural isomorphisms
For the m... |
CategoryTheory\NatTrans.lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baumann, Stephen Morgan, Scott Morrison, Floris van Doorn
-/
import Mathlib.Tactic.CategoryTheory.Reassoc
/-!
# Natural transformations
Defines natural transformations between fu... |
CategoryTheory\Noetherian.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.Subobject.Lattice
import Mathlib.CategoryTheory.EssentiallySmall
import Mathlib.CategoryTheory.Simple
/-!
# Artinian and noetherian cat... |
CategoryTheory\Opposites.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.Equivalence
/-!
# Opposite categories
We provide a category instance on `Cᵒᵖ`.
The morphisms `X ⟶ Y` are defined to be... |
CategoryTheory\PathCategory.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.EqToHom
import Mathlib.CategoryTheory.Quotient
import Mathlib.Combinatorics.Quiver.Path
/-!
# The category paths on a quiver.
When `C` ... |
CategoryTheory\PEmpty.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.DiscreteCategory
/-!
# The empty category
Defines a category structure on `PEmpty`, and the unique functor `PEmpty ⥤ C` ... |
CategoryTheory\PUnit.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.Functor.Const
import Mathlib.CategoryTheory.DiscreteCategory
/-!
# The category `Discrete PUnit`
We define `star : C ⥤ D... |
CategoryTheory\Quotient.lean | /-
Copyright (c) 2020 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import Mathlib.CategoryTheory.NatIso
import Mathlib.CategoryTheory.EqToHom
/-!
# Quotient category
Constructs the quotient of a category by an arbitrary family of relations... |
CategoryTheory\Simple.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.CategoryTheory.Limits.Shapes.ZeroMorphisms
import Mathlib.CategoryTheory.Limits.Shapes.Kernels
import Mathlib.CategoryTheory.Abelian.Bas... |
CategoryTheory\SingleObj.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.CategoryTheory.Endomorphism
import Mathlib.CategoryTheory.FinCategory.Basic
import Mathlib.CategoryTheory.Category.Cat
import Mathlib.Algebra.Categor... |
CategoryTheory\Skeletal.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.CategoryTheory.Adjunction.Basic
import Mathlib.CategoryTheory.Category.Preorder
import Mathlib.CategoryTheory.IsomorphismClasses
import Mathlib.CategoryThe... |
CategoryTheory\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.Comma.Arrow
import Mathlib.CategoryTheory.CommSq
/-!
# The category of commutative squares
In this file, we define a bundled version of `CommSq`... |
CategoryTheory\Subterminal.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.Terminal
import Mathlib.CategoryTheory.Subobject.MonoOver
/-!
# Su... |
CategoryTheory\Thin.lean | /-
Copyright (c) 2019 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.Functor.Category
import Mathlib.CategoryTheory.Iso
/-!
# Thin categories
A thin category (also known as a s... |
CategoryTheory\Types.lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison, Johannes Hölzl
-/
import Mathlib.CategoryTheory.EpiMono
import Mathlib.CategoryTheory.Functor.FullyFaithful
import Mathlib.Tactic.PPWithUniv
import Math... |
CategoryTheory\UnivLE.lean | /-
Copyright (c) 2023 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Logic.UnivLE
import Mathlib.CategoryTheory.EssentialImage
import Mathlib.CategoryTheory.Types
/-!
# Universe inequalities and essential surjectivity o... |
CategoryTheory\Whiskering.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.Iso
import Mathlib.CategoryTheory.Functor.Category
import Mathlib.CategoryTheory.Functor.FullyFaithful
/-!
# Whiskering
Given a functo... |
CategoryTheory\Widesubcategory.lean | /-
Copyright (c) 2024 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour
-/
import Mathlib.CategoryTheory.Functor.FullyFaithful
import Mathlib.CategoryTheory.MorphismProperty.Composition
/-!
# Wide subcategories
A wide subcategory of a ca... |
CategoryTheory\WithTerminal.lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith, Adam Topaz
-/
import Mathlib.CategoryTheory.Limits.Shapes.Terminal
import Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor
/-!
# `WithInitial` and `WithTermina... |
CategoryTheory\Yoneda.lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.CategoryTheory.Functor.Hom
import Mathlib.CategoryTheory.Products.Basic
import Mathlib.Data.ULift
import Mathlib.Logic.Function.ULift
/-!
# The Yoneda... |
CategoryTheory\Abelian\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, Johan Commelin, Scott Morrison
-/
import Mathlib.CategoryTheory.Limits.Constructions.Pullbacks
import Mathlib.CategoryTheory.Preadditive.Biproducts
import Mathlib.Categor... |
CategoryTheory\Abelian\EpiWithInjectiveKernel.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Homology.ShortComplex.ShortExact
import Mathlib.CategoryTheory.MorphismProperty.Composition
/-!
# Epimorphisms with an injective kernel
In this file, w... |
CategoryTheory\Abelian\Exact.lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Adam Topaz, Johan Commelin, Jakob von Raumer
-/
import Mathlib.Algebra.Homology.ImageToKernel
import Mathlib.Algebra.Homology.ShortComplex.Exact
import Mathlib.CategoryTh... |
CategoryTheory\Abelian\Ext.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
-/
import Mathlib.Algebra.Category.ModuleCat.Abelian
import Mathlib.Algebra.Homology.Opposite
import Mathlib.CategoryTheory.Abelian.LeftDerived
import Mathli... |
CategoryTheory\Abelian\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.Abelian.Basic
import Mathlib.CategoryTheory.Preadditive.FunctorCategory
import Mathlib.CategoryTheory.Limits.Shapes.FunctorCategory
impo... |
CategoryTheory\Abelian\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.Abelian.Subobject
import Mathlib.CategoryTheory.Limits.EssentiallySmall
import Mathlib.CategoryTheory.Preadditive.Injective
import Mathlib... |
CategoryTheory\Abelian\Images.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.Limits.Shapes.Kernels
/-!
# The abelian image and coimage.
In an abelian category we usually want the image of a morphis... |
CategoryTheory\Abelian\Injective.lean | /-
Copyright (c) 2022 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
import Mathlib.CategoryTheory.Abelian.Exact
import Mathlib.CategoryTheory.Preadditive.Injective
import Mathlib.CategoryTheory.Preadditive.Yoneda.Limits
import Mat... |
CategoryTheory\Abelian\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
-/
import Mathlib.CategoryTheory.Preadditive.InjectiveResolution
import Mathlib.Algebra.Homology.HomotopyCategory
import Mathlib.Data.Set.Subsingleton
import... |
CategoryTheory\Abelian\LeftDerived.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Riccardo Brasca, Adam Topaz, Jujian Zhang, Joël Riou
-/
import Mathlib.Algebra.Homology.Additive
import Mathlib.CategoryTheory.Abelian.ProjectiveResolution
/-!
# Left-... |
CategoryTheory\Abelian\NonPreadditive.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.FiniteProducts
import Mathlib.CategoryTheory.Limits.Shapes.Kernels
import Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Eq... |
CategoryTheory\Abelian\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
-/
import Mathlib.CategoryTheory.Abelian.Basic
import Mathlib.CategoryTheory.Preadditive.Opposite
import Mathlib.CategoryTheory.Limits.Opposites
/-!
# The opposite of a... |
CategoryTheory\Abelian\Projective.lean | /-
Copyright (c) 2022 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
import Mathlib.CategoryTheory.Abelian.Exact
import Mathlib.CategoryTheory.Preadditive.Yoneda.Projective
import Mathlib.CategoryTheory.Preadditive.Yoneda.Limits
im... |
CategoryTheory\Abelian\ProjectiveResolution.lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison, Jakob von Raumer, Joël Riou
-/
import Mathlib.CategoryTheory.Preadditive.ProjectiveResolution
import Mathlib.Algebra.Homology.HomotopyCategory
import Mathl... |
CategoryTheory\Abelian\Pseudoelements.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.Abelian.Exact
import Mathlib.CategoryTheory.Comma.Over
import Mathlib.Algebra.Category.ModuleCat.EpiMono
/-!
# Pseudoelements in abelian ... |
CategoryTheory\Abelian\Refinements.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.Algebra.Homology.ShortComplex.Exact
/-!
# Refinements
In order to prove injectivity/surjectivity/exactness properties for diagrams
in the category of abelian g... |
CategoryTheory\Abelian\RightDerived.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.Additive
import Mathlib.CategoryTheory.Abelian.InjectiveResolution
/-!
# Right-derived functors
We define the... |
CategoryTheory\Abelian\Subobject.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.Subobject.Limits
import Mathlib.CategoryTheory.Abelian.Basic
/-!
# Equivalence between subobjects and quotients in an abelian category
-... |
CategoryTheory\Abelian\Transfer.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.Abelian.Basic
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels
import Mathlib.CategoryTheory.Adjunction.Limits
/-!
# Trans... |
CategoryTheory\Abelian\DiagramLemmas\Four.lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Joël Riou
-/
import Mathlib.Algebra.Homology.ExactSequence
import Mathlib.CategoryTheory.Abelian.Refinements
/-!
# The four and five lemmas
Consider the following commu... |
CategoryTheory\Adjunction\AdjointFunctorTheorems.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.Generator
import Mathlib.CategoryTheory.Limits.ConeCategory
import Mathlib.CategoryTheory.Limits.Constructions.WeaklyInitial
import Mathlib.... |
CategoryTheory\Adjunction\Basic.lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Johan Commelin, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Equivalence
/-!
# Adjunctions between functors
`F ⊣ G` represents the data of an adjunction between two functo... |
CategoryTheory\Adjunction\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.Adjunction.Basic
import Mathlib.CategoryTheory.Comma.StructuredArrow
import Mathlib.CategoryTheory.PUnit
/-!
# Properties of comma categori... |
CategoryTheory\Adjunction\Evaluation.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.Functor.EpiMono
/-!
# Adjunctions involving evaluation
We show that evaluation of functo... |
CategoryTheory\Adjunction\FullyFaithful.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.Adjunction.Basic
import Mathlib.CategoryTheory.MorphismProperty.Basic
import Mathlib.CategoryTheory.EpiMono
/-!
# Adj... |
CategoryTheory\Adjunction\Lifting.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.Reflexive
import Mathlib.CategoryTheory.Monad.Adjunction
import Mathlib... |
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