path stringlengths 11 71 | content stringlengths 75 124k |
|---|---|
AlgebraicGeometry\Spec.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Justus Springer
-/
import Mathlib.Geometry.RingedSpace.LocallyRingedSpace
import Mathlib.AlgebraicGeometry.StructureSheaf
import Mathlib.RingTheory.Localization.Localiz... |
AlgebraicGeometry\Stalk.lean | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Fangming Li
-/
import Mathlib.AlgebraicGeometry.AffineScheme
/-!
# Stalks of a Scheme
Given a scheme `X` and a point `x : X`, `AlgebraicGeometry.Scheme.fromSpecStalk X x` i... |
AlgebraicGeometry\StructureSheaf.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Scott Morrison
-/
import Mathlib.AlgebraicGeometry.PrimeSpectrum.Basic
import Mathlib.Algebra.Category.Ring.Colimits
import Mathlib.Algebra.Category.Ring.Limits
import ... |
AlgebraicGeometry\Cover\Open.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.AlgebraicGeometry.OpenImmersion
/-!
# Open covers of schemes
This file provides the basic API for open covers of schemes.
## Main definition
- `AlgebraicG... |
AlgebraicGeometry\EllipticCurve\Affine.lean | /-
Copyright (c) 2023 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
import Mathlib.Algebra.Polynomial.Bivariate
import Mathlib.AlgebraicGeometry.EllipticCurve.Weierstrass
/-!
# Affine coordinates for Weierstrass c... |
AlgebraicGeometry\EllipticCurve\Group.lean | /-
Copyright (c) 2023 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
import Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian
import Mathlib.LinearAlgebra.FreeModule.Norm
import Mathlib.RingTheory.ClassGroup
/-!
# G... |
AlgebraicGeometry\EllipticCurve\Jacobian.lean | /-
Copyright (c) 2023 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
import Mathlib.Algebra.MvPolynomial.CommRing
import Mathlib.Algebra.MvPolynomial.PDeriv
import Mathlib.AlgebraicGeometry.EllipticCurve.Affine
impo... |
AlgebraicGeometry\EllipticCurve\Projective.lean | /-
Copyright (c) 2023 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
import Mathlib.AlgebraicGeometry.EllipticCurve.Affine
import Mathlib.Algebra.MvPolynomial.CommRing
import Mathlib.Algebra.MvPolynomial.PDeriv
/-!... |
AlgebraicGeometry\EllipticCurve\Weierstrass.lean | /-
Copyright (c) 2021 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, David Kurniadi Angdinata
-/
import Mathlib.Algebra.CubicDiscriminant
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.LinearCombination
/-!
# Weierstrass equations ... |
AlgebraicGeometry\EllipticCurve\DivisionPolynomial\Basic.lean | /-
Copyright (c) 2024 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
import Mathlib.AlgebraicGeometry.EllipticCurve.Group
import Mathlib.NumberTheory.EllipticDivisibilitySequence
/-!
# Division polynomials of Weier... |
AlgebraicGeometry\EllipticCurve\DivisionPolynomial\Degree.lean | /-
Copyright (c) 2024 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
import Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic
import Mathlib.Tactic.ComputeDegree
/-!
# Division polynomials of Weierst... |
AlgebraicGeometry\Modules\Presheaf.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.Category.ModuleCat.Presheaf
import Mathlib.AlgebraicGeometry.Scheme
import Mathlib.CategoryTheory.Sites.Whiskering
/-!
# The category of presheaves of m... |
AlgebraicGeometry\Modules\Sheaf.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.Category.ModuleCat.Sheaf.Abelian
import Mathlib.AlgebraicGeometry.Modules.Presheaf
/-!
# The category of sheaves of modules over a scheme
In this file... |
AlgebraicGeometry\Modules\Tilde.lean | /-
Copyright (c) 2024 Weihong Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Weihong Xu
-/
import Mathlib.Algebra.Module.LocalizedModule
import Mathlib.AlgebraicGeometry.StructureSheaf
import Mathlib.AlgebraicGeometry.Modules.Sheaf
import Mathlib.Algebra.Category.... |
AlgebraicGeometry\Morphisms\Affine.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.AlgebraicGeometry.Morphisms.QuasiSeparated
import Mathlib.AlgebraicGeometry.Morphisms.IsIso
/-!
# Affine morphisms of schemes
A morphism of schemes `f : X... |
AlgebraicGeometry\Morphisms\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.AlgebraicGeometry.AffineScheme
import Mathlib.AlgebraicGeometry.Pullbacks
import Mathlib.CategoryTheory.MorphismProperty.Limits
import Mathlib.Data.List.TFAE... |
AlgebraicGeometry\Morphisms\ClosedImmersion.lean | /-
Copyright (c) 2023 Jonas van der Schaaf. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston, Christian Merten, Jonas van der Schaaf
-/
import Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact
import Mathlib.AlgebraicGeometry.Morphisms.Preimmersion
/-!
... |
AlgebraicGeometry\Morphisms\Constructors.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.AlgebraicGeometry.Morphisms.Basic
import Mathlib.RingTheory.RingHomProperties
/-!
# Constructors for properties of morphisms between schemes
This file pro... |
AlgebraicGeometry\Morphisms\FiniteType.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.AlgebraicGeometry.Morphisms.RingHomProperties
import Mathlib.RingTheory.RingHom.FiniteType
/-!
# Morphisms of finite type
A morphism of schemes `f : X ⟶ Y`... |
AlgebraicGeometry\Morphisms\IsIso.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.AlgebraicGeometry.Morphisms.OpenImmersion
import Mathlib.Topology.IsLocalHomeomorph
/-!
# Being an isomorphism is local at the target
-/
open CategoryThe... |
AlgebraicGeometry\Morphisms\OpenImmersion.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.AlgebraicGeometry.Morphisms.UnderlyingMap
/-!
# Open immersions
A morphism is an open immersion if the underlying map of spaces is an open embedding
`f : ... |
AlgebraicGeometry\Morphisms\Preimmersion.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.AlgebraicGeometry.Morphisms.UnderlyingMap
import Mathlib.RingTheory.LocalProperties
/-!
# Preimmersions of schemes
A morphism of schemes `f : X ⟶ Y` is a ... |
AlgebraicGeometry\Morphisms\QuasiCompact.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.AlgebraicGeometry.Morphisms.Basic
import Mathlib.Topology.Spectral.Hom
import Mathlib.AlgebraicGeometry.Limits
/-!
# Quasi-compact morphisms
A morphism of ... |
AlgebraicGeometry\Morphisms\QuasiSeparated.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.AlgebraicGeometry.Morphisms.Constructors
import Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact
import Mathlib.Topology.QuasiSeparated
/-!
# Quasi-separate... |
AlgebraicGeometry\Morphisms\RingHomProperties.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.AlgebraicGeometry.Morphisms.Basic
import Mathlib.RingTheory.LocalProperties
/-!
# Properties of morphisms from properties of ring homs.
We provide the bas... |
AlgebraicGeometry\Morphisms\Separated.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.AlgebraicGeometry.Morphisms.ClosedImmersion
import Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated
import Mathlib.AlgebraicGeometry.Pullbacks
im... |
AlgebraicGeometry\Morphisms\UnderlyingMap.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.Topology.LocalAtTarget
import Mathlib.AlgebraicGeometry.Morphisms.Constructors
/-!
## Properties on the underlying functions of morphisms of schemes.
This... |
AlgebraicGeometry\Morphisms\UniversallyClosed.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.AlgebraicGeometry.Morphisms.Constructors
import Mathlib.Topology.LocalAtTarget
/-!
# Universally closed morphism
A morphism of schemes `f : X ⟶ Y` is unive... |
AlgebraicGeometry\PrimeSpectrum\Basic.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.RingTheory.PrimeSpectrum
import Mathlib.Topology.Irreducible
import Mathlib.Topology.Sets.Closeds
import Mathlib.Topology.Sober
import Mathlib.RingTheo... |
AlgebraicGeometry\PrimeSpectrum\IsOpenComapC.lean | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Mathlib.AlgebraicGeometry.PrimeSpectrum.Basic
import Mathlib.RingTheory.Polynomial.Basic
/-!
The morphism `Spec R[x] --> Spec R` induced by the natural inclusio... |
AlgebraicGeometry\PrimeSpectrum\Maximal.lean | /-
Copyright (c) 2022 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
import Mathlib.AlgebraicGeometry.PrimeSpectrum.Basic
import Mathlib.RingTheory.MaximalSpectrum
/-!
# Maximal spectrum of a commutative ring
The ... |
AlgebraicGeometry\PrimeSpectrum\Module.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.RingTheory.Support
import Mathlib.AlgebraicGeometry.PrimeSpectrum.Basic
/-!
# Subsets of prime spectra related to modules
## Main results
- `LocalizedMod... |
AlgebraicGeometry\PrimeSpectrum\Noetherian.lean | /-
Copyright (c) 2020 Filippo A. E. Nuccio. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Filippo A. E. Nuccio, Andrew Yang
-/
import Mathlib.AlgebraicGeometry.PrimeSpectrum.Basic
import Mathlib.Topology.NoetherianSpace
/-!
This file proves additional properties of t... |
AlgebraicGeometry\PrimeSpectrum\TensorProduct.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.RingTheory.SurjectiveOnStalks
import Mathlib.AlgebraicGeometry.PrimeSpectrum.Basic
/-!
# Lemmas regarding the prime spectrum of tensor products
## Main re... |
AlgebraicGeometry\ProjectiveSpectrum\Scheme.lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Andrew Yang
-/
import Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf
import Mathlib.AlgebraicGeometry.GammaSpecAdjunction
import Mathlib.RingTheory.GradedAlgeb... |
AlgebraicGeometry\ProjectiveSpectrum\StructureSheaf.lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology
import Mathlib.Topology.Sheaves.LocalPredicate
import Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalizatio... |
AlgebraicGeometry\ProjectiveSpectrum\Topology.lean | /-
Copyright (c) 2020 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Johan Commelin
-/
import Mathlib.RingTheory.GradedAlgebra.HomogeneousIdeal
import Mathlib.Topology.Category.TopCat.Basic
import Mathlib.Topology.Sets.Opens
import Mathlib.D... |
AlgebraicGeometry\Sites\BigZariski.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Adam Topaz
-/
import Mathlib.AlgebraicGeometry.Pullbacks
import Mathlib.CategoryTheory.Sites.Pretopology
import Mathlib.CategoryTheory.Sites.Canonical
/-!
# The big Zariski site ... |
AlgebraicTopology\AlternatingFaceMapComplex.lean | /-
Copyright (c) 2021 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Adam Topaz, Johan Commelin
-/
import Mathlib.Algebra.Homology.Additive
import Mathlib.AlgebraicTopology.MooreComplex
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Catego... |
AlgebraicTopology\CechNerve.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.AlgebraicTopology.SimplicialObject
import Mathlib.CategoryTheory.Comma.Arrow
import Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks
import Mathlib.CategoryT... |
AlgebraicTopology\ExtraDegeneracy.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.AlternatingFaceMapComplex
import Mathlib.AlgebraicTopology.SimplicialSet
import Mathlib.AlgebraicTopology.CechNerve
import Mathlib.Algebra.Homo... |
AlgebraicTopology\KanComplex.lean | /-
Copyright (c) 2023 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.AlgebraicTopology.SimplicialSet
/-!
# Kan complexes
In this file we give the definition of Kan complexes.
In `Mathlib/AlgebraicTopology/Quasicategor... |
AlgebraicTopology\MooreComplex.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.Homology.HomologicalComplex
import Mathlib.AlgebraicTopology.SimplicialObject
import Mathlib.CategoryTheory.Abelian.Basic
/-!
## Moore complex... |
AlgebraicTopology\Nerve.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.SimplicialSet
import Mathlib.CategoryTheory.ComposableArrows
/-!
# The nerve of a category
This file provides the definition of the nerve of... |
AlgebraicTopology\Quasicategory.lean | /-
Copyright (c) 2023 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.AlgebraicTopology.KanComplex
/-!
# Quasicategories
In this file we define quasicategories,
a common model of infinity categories.
We show that every... |
AlgebraicTopology\SimplexCategory.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Scott Morrison, Adam Topaz
-/
import Mathlib.Tactic.Linarith
import Mathlib.CategoryTheory.Skeletal
import Mathlib.Data.Fintype.Sort
import Mathlib.Order.Category.Nonem... |
AlgebraicTopology\SimplicialObject.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Scott Morrison, Adam Topaz
-/
import Mathlib.AlgebraicTopology.SimplexCategory
import Mathlib.CategoryTheory.Comma.Arrow
import Mathlib.CategoryTheory.Limits.FunctorCat... |
AlgebraicTopology\SimplicialSet.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Scott Morrison, Adam Topaz
-/
import Mathlib.AlgebraicTopology.SimplicialObject
import Mathlib.CategoryTheory.Limits.Shapes.Types
import Mathlib.CategoryTheory.Yoneda
i... |
AlgebraicTopology\SingularSet.lean | /-
Copyright (c) 2023 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Scott Morrison, Adam Topaz
-/
import Mathlib.AlgebraicTopology.SimplicialSet
import Mathlib.AlgebraicTopology.TopologicalSimplex
import Mathlib.CategoryTheory.Limits.Pr... |
AlgebraicTopology\SplitSimplicialObject.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.SimplicialObject
import Mathlib.CategoryTheory.Limits.Shapes.Products
/-!
# Split simplicial objects
In this file, we introduce the notion o... |
AlgebraicTopology\TopologicalSimplex.lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Adam Topaz
-/
import Mathlib.AlgebraicTopology.SimplexCategory
import Mathlib.Topology.Category.TopCat.Basic
import Mathlib.Topology.Instances.NNReal
/-!
# Topological sim... |
AlgebraicTopology\DoldKan\Compatibility.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.Equivalence
/-! Tools for compatibilities between Dold-Kan equivalences
The purpose of this file is to introduce tools which will enable the
con... |
AlgebraicTopology\DoldKan\Decomposition.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.DoldKan.PInfty
/-!
# Decomposition of the Q endomorphisms
In this file, we obtain a lemma `decomposition_Q` which expresses
explicitly the p... |
AlgebraicTopology\DoldKan\Degeneracies.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.DoldKan.Decomposition
import Mathlib.Tactic.FinCases
/-!
# Behaviour of P_infty with respect to degeneracies
For any `X : SimplicialObject C... |
AlgebraicTopology\DoldKan\Equivalence.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.DoldKan.EquivalencePseudoabelian
import Mathlib.AlgebraicTopology.DoldKan.Normalized
/-!
# The Dold-Kan correspondence
The Dold-Kan correspo... |
AlgebraicTopology\DoldKan\EquivalenceAdditive.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.DoldKan.NCompGamma
/-! The Dold-Kan equivalence for additive categories.
This file defines `Preadditive.DoldKan.equivalence` which is the equ... |
AlgebraicTopology\DoldKan\EquivalencePseudoabelian.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.DoldKan.EquivalenceAdditive
import Mathlib.AlgebraicTopology.DoldKan.Compatibility
import Mathlib.CategoryTheory.Idempotents.SimplicialObject
i... |
AlgebraicTopology\DoldKan\Faces.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.DoldKan.Homotopies
import Mathlib.Tactic.Ring
/-!
# Study of face maps for the Dold-Kan correspondence
In this file, we obtain the technical... |
AlgebraicTopology\DoldKan\FunctorGamma.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.SplitSimplicialObject
import Mathlib.AlgebraicTopology.DoldKan.PInfty
/-!
# Construction of the inverse functor of the Dold-Kan equivalence
... |
AlgebraicTopology\DoldKan\FunctorN.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.DoldKan.PInfty
/-!
# Construction of functors N for the Dold-Kan correspondence
In this file, we construct functors `N₁ : SimplicialObject C... |
AlgebraicTopology\DoldKan\GammaCompN.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.DoldKan.FunctorGamma
import Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject
import Mathlib.CategoryTheory.Idempotents.HomologicalComple... |
AlgebraicTopology\DoldKan\Homotopies.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Homology.Homotopy
import Mathlib.AlgebraicTopology.DoldKan.Notations
/-!
# Construction of homotopies for the Dold-Kan correspondence
(The general str... |
AlgebraicTopology\DoldKan\HomotopyEquivalence.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.DoldKan.Normalized
/-!
# The normalized Moore complex and the alternating face map complex are homotopy equivalent
In this file, when the ca... |
AlgebraicTopology\DoldKan\NCompGamma.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.DoldKan.GammaCompN
import Mathlib.AlgebraicTopology.DoldKan.NReflectsIso
/-! The unit isomorphism of the Dold-Kan equivalence
In order to con... |
AlgebraicTopology\DoldKan\Normalized.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.DoldKan.FunctorN
/-!
# Comparison with the normalized Moore complex functor
In this file, we show that when the category `A` is abelian,
the... |
AlgebraicTopology\DoldKan\Notations.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.AlternatingFaceMapComplex
/-!
# Notations for the Dold-Kan equivalence
This file defines the notation `K[X] : ChainComplex C ℕ` for the alte... |
AlgebraicTopology\DoldKan\NReflectsIso.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.DoldKan.FunctorN
import Mathlib.AlgebraicTopology.DoldKan.Decomposition
import Mathlib.CategoryTheory.Idempotents.HomologicalComplex
import Mat... |
AlgebraicTopology\DoldKan\PInfty.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.DoldKan.Projections
import Mathlib.CategoryTheory.Idempotents.FunctorCategories
import Mathlib.CategoryTheory.Idempotents.FunctorExtension
/-!... |
AlgebraicTopology\DoldKan\Projections.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.DoldKan.Faces
import Mathlib.CategoryTheory.Idempotents.Basic
/-!
# Construction of projections for the Dold-Kan correspondence
In this file... |
AlgebraicTopology\DoldKan\SplitSimplicialObject.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.SplitSimplicialObject
import Mathlib.AlgebraicTopology.DoldKan.Degeneracies
import Mathlib.AlgebraicTopology.DoldKan.FunctorN
/-!
# Split sim... |
AlgebraicTopology\FundamentalGroupoid\Basic.lean | /-
Copyright (c) 2021 Shing Tak Lam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shing Tak Lam
-/
import Mathlib.CategoryTheory.Category.Grpd
import Mathlib.CategoryTheory.Groupoid
import Mathlib.Topology.Category.TopCat.Basic
import Mathlib.Topology.Homotopy.Path
i... |
AlgebraicTopology\FundamentalGroupoid\FundamentalGroup.lean | /-
Copyright (c) 2021 Mark Lavrentyev. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mark Lavrentyev
-/
import Mathlib.CategoryTheory.Groupoid
import Mathlib.Topology.Category.TopCat.Basic
import Mathlib.Topology.Connected.PathConnected
import Mathlib.Topology.Homotop... |
AlgebraicTopology\FundamentalGroupoid\InducedMaps.lean | /-
Copyright (c) 2022 Praneeth Kolichala. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Praneeth Kolichala
-/
import Mathlib.Topology.Homotopy.Equiv
import Mathlib.CategoryTheory.Equivalence
import Mathlib.AlgebraicTopology.FundamentalGroupoid.Product
/-!
# Homotopic... |
AlgebraicTopology\FundamentalGroupoid\Product.lean | /-
Copyright (c) 2022 Praneeth Kolichala. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Praneeth Kolichala
-/
import Mathlib.CategoryTheory.Groupoid
import Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic
import Mathlib.Topology.Category.TopCat.Limits.Products
impo... |
AlgebraicTopology\FundamentalGroupoid\PUnit.lean | /-
Copyright (c) 2022 Praneeth Kolichala. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Praneeth Kolichala
-/
import Mathlib.CategoryTheory.PUnit
import Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic
/-!
# Fundamental groupoid of punit
The fundamental groupoid ... |
AlgebraicTopology\FundamentalGroupoid\SimplyConnected.lean | /-
Copyright (c) 2022 Praneeth Kolichala. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Praneeth Kolichala
-/
import Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps
import Mathlib.Topology.Homotopy.Contractible
import Mathlib.CategoryTheory.PUnit
import Math... |
AlgebraicTopology\SimplicialCategory\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.AlgebraicTopology.SimplicialSet.Monoidal
import Mathlib.CategoryTheory.Enriched.Basic
/-!
# Simplicial categories
A simplicial category is a category `C` that ... |
AlgebraicTopology\SimplicialSet\Monoidal.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Jack McKoen
-/
import Mathlib.AlgebraicTopology.SimplicialSet
import Mathlib.CategoryTheory.ChosenFiniteProducts.FunctorCategory
import Mathlib.CategoryTheory.Monoidal.Types.Basi... |
Analysis\BoundedVariation.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.Calculus.FDeriv.Add
import Mathlib.Analysis.Calculus.FDeriv.Equiv
import Mathlib.Analysis.Calculus.FDeriv.Prod
import Mathlib.Analysis.C... |
Analysis\ConstantSpeed.lean | /-
Copyright (c) 2023 Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémi Bottinelli
-/
import Mathlib.Data.Set.Function
import Mathlib.Analysis.BoundedVariation
/-!
# Constant speed
This file defines the notion of constant (and unit) speed for a fun... |
Analysis\Convolution.lean | /-
Copyright (c) 2022 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Mathlib.Analysis.Calculus.ContDiff.Basic
import Mathlib.Analysis.Calculus.ParametricIntegral
import Mathlib.MeasureTheory.Constructions.Prod.Integral
impor... |
Analysis\Hofer.lean | /-
Copyright (c) 2020 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Analysis.SpecificLimits.Basic
/-!
# Hofer's lemma
This is an elementary lemma about complete metric spaces. It is motivated by an
application to the ... |
Analysis\Matrix.lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth, Eric Wieser
-/
import Mathlib.Analysis.Normed.Lp.PiLp
import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
# Matrices as a normed space
In this file we provide the fo... |
Analysis\MeanInequalities.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
-/
import Mathlib.Analysis.Convex.Jensen
import Mathlib.Analysis.Convex.SpecificFunctions.Basic
import Mathlib.Analysis.SpecialFunctio... |
Analysis\MeanInequalitiesPow.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
-/
import Mathlib.Analysis.Convex.Jensen
import Mathlib.Analysis.Convex.Mul
import Mathlib.Analysis.Convex.SpecificFunctions.Basic
imp... |
Analysis\MellinInversion.lean | /-
Copyright (c) 2024 Lawrence Wu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lawrence Wu
-/
import Mathlib.Analysis.Fourier.Inversion
/-!
# Mellin inversion formula
We derive the Mellin inversion formula as a consequence of the Fourier inversion formula.
## Mai... |
Analysis\MellinTransform.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.ImproperIntegrals
import Mathlib.Analysis.Calculus.ParametricIntegral
import Mathlib.MeasureTheory.Measure.Haar.NormedSpace
... |
Analysis\Oscillation.lean | /-
Copyright (c) 2024 James Sundstrom. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: James Sundstrom
-/
import Mathlib.Topology.EMetricSpace.Basic
import Mathlib.Order.WellFoundedSet
/-!
# Oscillation
In this file we define the oscillation of a function `f: E → F` a... |
Analysis\PSeries.lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
import Mathlib.Analysis.SpecialFunctions.Pow.Continuity
import Mathlib.Analysis.SumOverResidueClass
/-!
#... |
Analysis\PSeriesComplex.lean | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
import Mathlib.Analysis.PSeries
import Mathlib.Analysis.Normed.Module.FiniteDimension
import Mathlib.Data.Complex.FiniteDimensional
/-!
# Convergence of `p`-series ... |
Analysis\Quaternion.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Eric Wieser
-/
import Mathlib.Algebra.Quaternion
import Mathlib.Analysis.InnerProductSpace.Basic
import Mathlib.Analysis.InnerProductSpace.PiL2
import Mathlib.Topolog... |
Analysis\Seminorm.lean | /-
Copyright (c) 2019 Jean Lo. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean Lo, Yaël Dillies, Moritz Doll
-/
import Mathlib.Data.Real.Pointwise
import Mathlib.Analysis.Convex.Function
import Mathlib.Analysis.LocallyConvex.Basic
/-!
# Seminorms
This file define... |
Analysis\Subadditive.lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Topology.Instances.Real
import Mathlib.Order.Filter.Archimedean
/-!
# Convergence of subadditive sequences
A subadditive sequence `u : ℕ → ℝ` i... |
Analysis\SumIntegralComparisons.lean | /-
Copyright (c) 2022 Kevin H. Wilson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin H. Wilson
-/
import Mathlib.MeasureTheory.Integral.IntervalIntegral
import Mathlib.Data.Set.Function
/-!
# Comparing sums and integrals
## Summary
It is often the case that e... |
Analysis\SumOverResidueClass.lean | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import Mathlib.Data.ZMod.Basic
import Mathlib.Topology.Instances.ENNReal
import Mathlib.Analysis.Normed.Field.Basic
/-!
# Sums over residue classes
We consider infini... |
Analysis\Analytic\Basic.lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yury Kudryashov
-/
import Mathlib.Algebra.Star.Order
import Mathlib.Analysis.Calculus.FormalMultilinearSeries
import Mathlib.Analysis.SpecificLimits.Normed
import... |
Analysis\Analytic\Composition.lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Johan Commelin
-/
import Mathlib.Analysis.Analytic.Basic
import Mathlib.Combinatorics.Enumerative.Composition
/-!
# Composition of analytic functions
In this fi... |
Analysis\Analytic\Constructions.lean | /-
Copyright (c) 2023 Geoffrey Irving. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler, Geoffrey Irving
-/
import Mathlib.Analysis.Analytic.Composition
import Mathlib.Analysis.Analytic.Linear
import Mathlib.Analysis.NormedSpace.OperatorNorm.Mul
/-!
# Var... |
Analysis\Analytic\CPolynomial.lean | /-
Copyright (c) 2023 Sophie Morel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sophie Morel
-/
import Mathlib.Analysis.Analytic.Basic
/-! We specialize the theory fo analytic functions to the case of functions that admit a
development given by a *finite* formal mu... |
Analysis\Analytic\Inverse.lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Analysis.Analytic.Composition
/-!
# Inverse of analytic functions
We construct the left and right inverse of a formal multilinear series with ... |
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