path stringlengths 11 71 | content stringlengths 75 124k |
|---|---|
Algebra\Group\Submonoid\Pointwise.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Group.Submonoid.Membership
import Mathlib.Algebra.Order.BigOperators.Group.List
import Mathlib.Data.Set.Pointwise.SMul
import Mathlib.Order.WellFound... |
Algebra\Group\Submonoid\Units.lean | /-
Copyright (c) 2023 Wrenna Robson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wrenna Robson
-/
import Mathlib.Algebra.Group.Submonoid.Operations
import Mathlib.Algebra.Group.Submonoid.Pointwise
import Mathlib.Algebra.Group.Subgroup.Basic
/-!
# Submonoid of unit... |
Algebra\Group\Subsemigroup\Basic.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
Amelia Livingston, Yury Kudryashov, Yakov Pechersky
-/
import Mathlib.Algebra.Group.Hom.Defs
import Mathlib.Da... |
Algebra\Group\Subsemigroup\Membership.lean | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Group.Subsemigroup.Basic
/-!
# Subsemigroups: membership criteria
In this file we prove various facts about membership in a subsemigroup.
The i... |
Algebra\Group\Subsemigroup\Operations.lean | /-
Copyright (c) 2022 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
Amelia Livingston, Yury Kudryashov, Yakov Pechersky, Jireh Loreaux
-/
import Mathlib.Algebra.Group.Prod
impor... |
Algebra\Group\Units\Equiv.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Equiv.Basic
import Mathlib.Algebra.Group.Units.Hom
/-!
# Multiplicative and additive equivalence acting ... |
Algebra\Group\Units\Hom.lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Chris Hughes, Kevin Buzzard
-/
import Mathlib.Algebra.Group.Hom.Defs
import Mathlib.Algebra.Group.Units
/-!
# Monoid homomorphisms and units
This file allows to lift ... |
Algebra\Group\WithOne\Basic.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johan Commelin
-/
import Mathlib.Algebra.Group.Equiv.Basic
import Mathlib.Algebra.Group.WithOne.Defs
/-!
# More operations on `WithOne` and `WithZero`
This file defin... |
Algebra\Group\WithOne\Defs.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johan Commelin
-/
import Mathlib.Algebra.Group.Defs
import Mathlib.Data.Option.Defs
import Mathlib.Logic.Nontrivial.Basic
import Mathlib.Tactic.Common
/-!
# Adjoining ... |
Algebra\GroupPower\IterateHom.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.Group.Action.Opposite
import Mathlib.Algebra.Group.Int
import Mathlib.Algebra.Group.Nat
import Mathlib.Logic.Function.Iterate
import Mathlib.... |
Algebra\GroupWithZero\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.Algebra.Group.Basic
import Mathlib.Algebra.GroupWithZero.NeZero
import Mathlib.Logic.Unique
/-!
# Groups with an adjoined zero element
This file desc... |
Algebra\GroupWithZero\Center.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Jireh Loreaux
-/
import Mathlib.Algebra.Group.Center
import Mathlib.Algebra.GroupWithZero.Units.Basic
/-!
# Center of a group with zero
-/
assert_not_exists Finset
assert_n... |
Algebra\GroupWithZero\Commute.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.GroupWithZero.Semiconj
import Mathlib.Algebra.Group.Commute.Units
import Mathlib.Tactic.Nontriviality
/-!
# Lemmas about commuting elements in... |
Algebra\GroupWithZero\Conj.lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import Mathlib.Algebra.Group.Conj
import Mathlib.Algebra.GroupWithZero.Units.Basic
/-!
# Conjugacy in a group with zero
-/
assert_not_exists Multiset
-- TODO
-- ass... |
Algebra\GroupWithZero\Defs.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.Group.Defs
import Mathlib.Logic.Function.Basic
import Mathlib.Logic.Nontrivial.Defs
import Mathlib.Tactic.SplitIfs
/-!
# Typeclasses for group... |
Algebra\GroupWithZero\Divisibility.lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Amelia Livingston, Yury Kudryashov,
Neil Strickland, Aaron Anderson
-/
import Mathlib.Algebra.GroupWithZero.Units.Basic
import Mathli... |
Algebra\GroupWithZero\Hom.lean | /-
Copyright (c) 2020 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Group.Equiv.Basic
import Mathlib.Algebra.GroupWithZero.Basic
import Mathlib.Algebra.NeZero
/-!
# Monoid with zero and group with zero homomorphis... |
Algebra\GroupWithZero\Indicator.lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Indicator
import Mathlib.Algebra.GroupWithZero.Basic
/-!
# Indicator functions and support of a function in groups with z... |
Algebra\GroupWithZero\InjSurj.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.Group.InjSurj
import Mathlib.Algebra.GroupWithZero.NeZero
/-!
# Lifting groups with zero along injective/surjective maps
-/
assert_not_exist... |
Algebra\GroupWithZero\Invertible.lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.Algebra.Group.Invertible.Basic
import Mathlib.Algebra.GroupWithZero.Units.Basic
/-!
# Theorems about invertible elements in a `GroupWithZero`
We intentiona... |
Algebra\GroupWithZero\NeZero.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.GroupWithZero.Defs
import Mathlib.Algebra.NeZero
/-!
# `NeZero 1` in a nontrivial `MulZeroOneClass`.
This file exists to minimize the depende... |
Algebra\GroupWithZero\NonZeroDivisors.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Devon Tuma, Oliver Nash
-/
import Mathlib.Algebra.Associated.Basic
import Mathlib.Algebra.Group.Action.Opposite
import Mathlib.Algebra.Group.Submonoid.Membership
import Mathlib.A... |
Algebra\GroupWithZero\Opposite.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.Group.Opposite
import Mathlib.Algebra.GroupWithZero.Defs
/-!
# Opposites of groups with zero
-/
assert_not_exists Ring
variable {α : Type*}
namespace... |
Algebra\GroupWithZero\Pi.lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.GroupWithZero.Defs
import Mathlib.Algebra.Group.Hom.Defs
import Mathlib.Algebra.Group.Pi.Basic
/-!
# Pi instances for groups with zero
This file de... |
Algebra\GroupWithZero\Prod.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Yaël Dillies
-/
import Mathlib.Algebra.Group.Prod
import Mathlib.Algebra.GroupWithZero.Hom
import Mathlib.Algebra.GroupWithZero.Units.Basic
/-!
# Products of monoids with ze... |
Algebra\GroupWithZero\Semiconj.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.GroupWithZero.Units.Basic
import Mathlib.Algebra.Group.Semiconj.Units
import Mathlib.Init.Classical
/-!
# Lemmas about semiconjugate elements ... |
Algebra\GroupWithZero\ULift.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.ULift
import Mathlib.Algebra.GroupWithZero.InjSurj
/-!
# `ULift` instances for groups and monoids with zero
This file defines instances... |
Algebra\GroupWithZero\WithZero.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johan Commelin
-/
import Mathlib.Algebra.Group.WithOne.Defs
import Mathlib.Algebra.GroupWithZero.Hom
import Mathlib.Algebra.GroupWithZero.Units.Basic
import Mathlib.Dat... |
Algebra\GroupWithZero\Action\Defs.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Action.Defs
import Mathlib.Algebra.Group.Hom.Defs
import Mathlib.Algebra.Group.TypeTags
import Mathlib.Algebra.Opposites
imp... |
Algebra\GroupWithZero\Action\Opposite.lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Group.Action.Opposite
import Mathlib.Algebra.GroupWithZero.Action.Defs
import Mathlib.Algebra.GroupWithZero.NeZero
/-!
# Scalar actions on and by `M... |
Algebra\GroupWithZero\Action\Pi.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
-/
import Mathlib.Algebra.Group.Action.Pi
import Mathlib.Algebra.GroupWithZero.Action.Defs
import Mathlib.Algebra.GroupWithZero.Defs
import Mathlib.Tactic.Comm... |
Algebra\GroupWithZero\Action\Prod.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot, Eric Wieser
-/
import Mathlib.Algebra.Group.Action.Prod
import Mathlib.Algebra.GroupWithZero.Action.Defs
/-!
# Prod instances for multiplicative actions with... |
Algebra\GroupWithZero\Action\Units.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Group.Action.Units
import Mathlib.Algebra.GroupWithZero.Action.Defs
/-!
# Multiplicative actions with zero on and by `Mˣ`
This file provides the mu... |
Algebra\GroupWithZero\Units\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.Algebra.Group.Units
import Mathlib.Algebra.GroupWithZero.Basic
import Mathlib.Logic.Equiv.Defs
import Mathlib.Tactic.Contrapose
import Mathlib.Tactic.N... |
Algebra\GroupWithZero\Units\Equiv.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Units.Equiv
import Mathlib.Algebra.GroupWithZero.Units.Basic
/-!
# Multiplication by a nonzero element i... |
Algebra\GroupWithZero\Units\Lemmas.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.Group.Units.Hom
import Mathlib.Algebra.GroupWithZero.Action.Units
import Mathlib.Algebra.GroupWithZero.Commute
import Mathlib.Algebra.GroupWith... |
Algebra\Homology\Additive.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.Single
import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
/-!
# Homology is an additive functor
When `V` is preadditive, `Hom... |
Algebra\Homology\Augment.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.Single
/-!
# Augmentation and truncation of `ℕ`-indexed (co)chain complexes.
-/
noncomputable section
open CategoryTheory Limits H... |
Algebra\Homology\Bifunctor.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.TotalComplex
import Mathlib.CategoryTheory.GradedObject.Bifunctor
/-!
# The action of a bifunctor on homological complexes
Given a bifunctor `... |
Algebra\Homology\BifunctorHomotopy.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.Bifunctor
import Mathlib.Algebra.Homology.Homotopy
/-!
# The action of a bifunctor on homological complexes factors through homotopies
Given a... |
Algebra\Homology\BifunctorShift.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.Bifunctor
import Mathlib.Algebra.Homology.TotalComplexShift
/-!
# Behavior of the action of a bifunctor on cochain complexes with respect to sh... |
Algebra\Homology\CommSq.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Preadditive.Biproducts
/-!
# Relation between pullback/pushout squares and kernel/cok... |
Algebra\Homology\ComplexShape.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
-/
import Mathlib.Algebra.Group.Defs
import Mathlib.Logic.Relation
/-!
# Shapes of homological complexes
We define a structure `ComplexShape ι` for des... |
Algebra\Homology\ComplexShapeSigns.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.ComplexShape
import Mathlib.Algebra.Ring.NegOnePow
/-! Signs in constructions on homological complexes
In this file, we shall introduce variou... |
Algebra\Homology\ConcreteCategory.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Homology.HomologySequence
import Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory
/-!
# Homology of complexes in concrete categories
The homology... |
Algebra\Homology\DifferentialObject.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.CategoryTheory.DifferentialObject
/-!
# Homological complexes are differential graded objects.
We ... |
Algebra\Homology\ExactSequence.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
import Mathlib.CategoryTheory.ComposableArrows
/-!
# Exact sequences
A sequence of `n` composable arrows `S : ComposableArr... |
Algebra\Homology\Functor.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.Algebra.Homology.HomologicalComplex
/-!
# Complexes in functor categories
We can view a complex valued in a functor category `T ⥤ V` as
a functor fro... |
Algebra\Homology\HomologicalBicomplex.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.HomologicalComplex
/-!
# Bicomplexes
Given a category `C` with zero morphisms and two complex shapes
`c₁ : ComplexShape I... |
Algebra\Homology\HomologicalComplex.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
-/
import Mathlib.Algebra.Homology.ComplexShape
import Mathlib.CategoryTheory.Subobject.Limits
import Mathlib.CategoryTheory.GradedObject
import Mathlib.... |
Algebra\Homology\HomologicalComplexAbelian.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.Additive
import Mathlib.Algebra.Homology.HomologicalComplexLimits
import Mathlib.Algebra.Homology.ShortComplex.ShortExact
/-! # THe category of... |
Algebra\Homology\HomologicalComplexBiprod.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.HomologicalComplexLimits
import Mathlib.Algebra.Homology.Additive
/-! Binary biproducts of homological complexes
In this file, it is shown tha... |
Algebra\Homology\HomologicalComplexLimits.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.Single
import Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits
import Mathlib.CategoryTheory.Limits.Preserves.Finite
import Mathlib.CategoryThe... |
Algebra\Homology\HomologySequence.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.HomologicalComplex
import Mathlib.Algebra.Homology.ShortComplex.SnakeLemma
import Mathlib.Algebra.Homology.ShortComplex.ShortExact
... |
Algebra\Homology\HomologySequenceLemmas.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.HomologySequence
import Mathlib.Algebra.Homology.QuasiIso
import Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four
/-!
# Consequences of the ho... |
Algebra\Homology\Homotopy.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.Linear
import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
import Mathlib.Tactic.Abel
/-!
# Chain homotopies
We define c... |
Algebra\Homology\HomotopyCategory.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.Homotopy
import Mathlib.Algebra.Homology.Linear
import Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy
import Mathlib.CategoryThe... |
Algebra\Homology\HomotopyCofiber.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.HomologicalComplexBiprod
import Mathlib.Algebra.Homology.Homotopy
import Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy
/-! The homotopy ... |
Algebra\Homology\ImageToKernel.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.Subobject.Limits
/-!
# Image-to-kernel comparison maps
Whenever `f : A ⟶ B` and `g : B ⟶ C` satisfy `w : f ≫ g = 0`,
we have `image_le... |
Algebra\Homology\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.Algebra.Homology.Additive
import Mathlib.CategoryTheory.Linear.LinearFunctor
/-!
# The category of homological complexes is linear
In this file, we define the ... |
Algebra\Homology\LocalCohomology.lean | /-
Copyright (c) 2023 Emily Witt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Emily Witt, Scott Morrison, Jake Levinson, Sam van Gool
-/
import Mathlib.RingTheory.Ideal.Basic
import Mathlib.Algebra.Category.ModuleCat.Colimits
import Mathlib.Algebra.Category.ModuleCa... |
Algebra\Homology\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.Algebra.Homology.HomotopyCofiber
import Mathlib.Algebra.Homology.HomotopyCategory
import Mathlib.Algebra.Homology.QuasiIso
import Mathlib.CategoryTheory.Localiz... |
Algebra\Homology\Opposite.lean | /-
Copyright (c) 2022 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Amelia Livingston, Joël Riou
-/
import Mathlib.CategoryTheory.Abelian.Opposite
import Mathlib.Algebra.Homology.Additive
import Mathlib.Algebra.Homology.ImageToKernel... |
Algebra\Homology\QuasiIso.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.Homotopy
/-!
# Quasi-isomorphisms
A chain map is a quasi-isomorphism if it induces isomorphisms on homology.
-/
open C... |
Algebra\Homology\Refinements.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.Abelian.Refinements
import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
/-!
# Refinements
This file contains lemmas about "refineme... |
Algebra\Homology\Single.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
/-!
# Homological complexes supported in a single degree
We define `single V j c : V ⥤ HomologicalComplex V c`,
w... |
Algebra\Homology\SingleHomology.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.Single
import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
/-!
# The homology of single complexes
The main definition in this file ... |
Algebra\Homology\TotalComplex.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.Linear.Basic
import Mathlib.Algebra.Homology.ComplexShapeSigns
import Mathlib.Algebra.Homology.HomologicalBicomplex
/-!
# The total complex of a ... |
Algebra\Homology\TotalComplexShift.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.HomotopyCategory.Shift
import Mathlib.Algebra.Homology.TotalComplex
/-!
# Behaviour of the total complex with respect to shifts
There are two ... |
Algebra\Homology\TotalComplexSymmetry.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.TotalComplex
/-! The symmetry of the total complex of a bicomplex
Let `K : HomologicalComplex₂ C c₁ c₂` be a bicomplex. If we assume both
`[To... |
Algebra\Homology\DerivedCategory\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.Algebra.Homology.HomotopyCategory.HomologicalFunctor
import Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence
import Mathlib.Algebra.Homology.HomotopyCateg... |
Algebra\Homology\DerivedCategory\ExactFunctor.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.DerivedCategory.Basic
/-!
# An exact functor induces a functor on derived categories
In this file, we show that if `F : C₁ ⥤ C₂` is an exact f... |
Algebra\Homology\DerivedCategory\Ext.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.DerivedCategory.Basic
import Mathlib.CategoryTheory.Localization.SmallShiftedHom
/-!
# Ext groups in abelian categories
Let `C` be an abelian ... |
Algebra\Homology\DerivedCategory\HomologySequence.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.DerivedCategory.Basic
/-!
# The homology sequence
In this file, we construct `homologyFunctor C n : DerivedCategory C ⥤ C` for all `n : ℤ`,
s... |
Algebra\Homology\DerivedCategory\ShortExact.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.HomotopyCategory.ShortExact
import Mathlib.Algebra.Homology.DerivedCategory.Basic
/-!
# The distinguished triangle attached to a short exact se... |
Algebra\Homology\DerivedCategory\SingleTriangle.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.DerivedCategory.ShortExact
/-!
# The distinguished triangle of a short exact sequence in an abelian category
Given a short exact short complex... |
Algebra\Homology\Embedding\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.Algebra.Homology.ComplexShape
import Mathlib.Algebra.Order.Ring.Nat
import Mathlib.Algebra.Ring.Int
/-! # Embeddings of complex shapes
Given two complex shapes... |
Algebra\Homology\Embedding\Boundary.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.Embedding.Basic
import Mathlib.Algebra.Homology.HomologicalComplex
/-!
# Boundary of an embedding of complex shapes
In the file `Mathlib.Algeb... |
Algebra\Homology\Embedding\Extend.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.Embedding.Basic
import Mathlib.Algebra.Homology.HomologicalComplex
/-!
# The extension of a homological complex by an embedding of complex shap... |
Algebra\Homology\Embedding\IsSupported.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.Embedding.Basic
import Mathlib.Algebra.Homology.Opposite
import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
/-! # Support of homol... |
Algebra\Homology\Embedding\Restriction.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.Embedding.Basic
import Mathlib.Algebra.Homology.Additive
/-!
# The restriction functor of an embedding of complex shapes
Given `c` and `c'` co... |
Algebra\Homology\Embedding\TruncGE.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.Embedding.Boundary
import Mathlib.Algebra.Homology.Embedding.Extend
import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
/-!
# The c... |
Algebra\Homology\Factorizations\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.Algebra.Homology.HomologicalComplex
import Mathlib.CategoryTheory.Abelian.EpiWithInjectiveKernel
/-!
# Basic definitions for factorizations lemmas
We define th... |
Algebra\Homology\HomotopyCategory\DegreewiseSplit.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.HomotopyCategory.Pretriangulated
/-! Degreewise split exact sequences of cochain complexes
The main result of this file is the lemma
`Homotopy... |
Algebra\Homology\HomotopyCategory\HomComplex.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.Homotopy
import Mathlib.Algebra.Ring.NegOnePow
import Mathlib.Algebra.Category.Grp.Preadditive
import Mathlib.Tactic.Linarith
import Mathlib.Cat... |
Algebra\Homology\HomotopyCategory\HomComplexShift.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.HomotopyCategory.HomComplex
import Mathlib.Algebra.Homology.HomotopyCategory.Shift
/-! Shifting cochains
Let `C` be a preadditive category. Gi... |
Algebra\Homology\HomotopyCategory\HomologicalFunctor.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.HomologicalComplexAbelian
import Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit
import Mathlib.Algebra.Homology.HomologySequence
impo... |
Algebra\Homology\HomotopyCategory\MappingCone.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.HomotopyCategory.HomComplex
import Mathlib.Algebra.Homology.HomotopyCofiber
/-! # The mapping cone of a morphism of cochain complexes
In this ... |
Algebra\Homology\HomotopyCategory\Pretriangulated.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.HomotopyCategory.MappingCone
import Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift
import Mathlib.CategoryTheory.Triangulated.Functor... |
Algebra\Homology\HomotopyCategory\Shift.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.HomotopyCategory
import Mathlib.Algebra.Ring.NegOnePow
import Mathlib.CategoryTheory.Shift.Quotient
import Mathlib.CategoryTheory.Linear.LinearF... |
Algebra\Homology\HomotopyCategory\ShiftSequence.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.InducedShiftSequence
import Mathlib.CategoryTheory.Shift.Localization
import Mathlib.Algebra.Homology.HomotopyCategory.Shift
import Mathlib.... |
Algebra\Homology\HomotopyCategory\ShortExact.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.HomotopyCategory.HomologicalFunctor
import Mathlib.Algebra.Homology.HomotopyCategory.ShiftSequence
import Mathlib.Algebra.Homology.HomologySeque... |
Algebra\Homology\HomotopyCategory\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.Algebra.Homology.HomotopyCategory.Shift
import Mathlib.CategoryTheory.Shift.SingleFunctors
/-!
# Single functors from the homotopy category
Let `C` be a preadd... |
Algebra\Homology\HomotopyCategory\Triangulated.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.HomotopyCategory.Pretriangulated
import Mathlib.CategoryTheory.Triangulated.Triangulated
import Mathlib.CategoryTheory.ComposableArrows
/-! The... |
Algebra\Homology\ShortComplex\Ab.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.ShortExact
import Mathlib.Algebra.Category.Grp.Abelian
import Mathlib.Algebra.Category.Grp.Kernels
import Mathlib.Algebra.Exact
/-... |
Algebra\Homology\ShortComplex\Abelian.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.Homology
import Mathlib.CategoryTheory.Abelian.Basic
/-!
# Abelian categories have homology
In this file, it is shown that all s... |
Algebra\Homology\ShortComplex\Basic.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.Limits.Preserves.Shapes.Zero
/-!
# Short complexes
This file defines the category `ShortComplex C` of diagrams
`X₁ ⟶ X₂ ⟶ X₃` such that the com... |
Algebra\Homology\ShortComplex\ConcreteCategory.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Homology.ShortComplex.Ab
import Mathlib.Algebra.Homology.ShortComplex.ExactFunctor
import Mathlib.Algebra.Homology.ShortComplex.SnakeLemma
import Mathlib... |
Algebra\Homology\ShortComplex\Exact.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.PreservesHomology
import Mathlib.Algebra.Homology.ShortComplex.Abelian
import Mathlib.Algebra.Homology.ShortComplex.QuasiIso
import... |
Algebra\Homology\ShortComplex\ExactFunctor.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Jujian Zhang
-/
import Mathlib.Algebra.Homology.ShortComplex.PreservesHomology
import Mathlib.Algebra.Homology.ShortComplex.ShortExact
import Mathlib.Algebra.Homology.ShortComple... |
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