path stringlengths 11 71 | content stringlengths 75 124k |
|---|---|
Algebra\Category\Grp\Biproducts.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Algebra.Group.Pi.Lemmas
import Mathlib.Algebra.Category.Grp.Preadditive
import Mathlib.CategoryTheory.Preadditive.Biproducts
import Mathlib.Algebra.Cat... |
Algebra\Category\Grp\Colimits.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Algebra.Category.Grp.Preadditive
import Mathlib.GroupTheory.QuotientGroup
import Mathlib.CategoryTheory.Limits.Shapes.Kernels
import Mathlib.CategoryTh... |
Algebra\Category\Grp\EnoughInjectives.lean | /-
Copyright (c) 2023 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Junyan Xu
-/
import Mathlib.Algebra.Module.CharacterModule
import Mathlib.Algebra.Category.Grp.EquivalenceGroupAddGroup
import Mathlib.Algebra.Category.Grp.EpiMono
/-!
#... |
Algebra\Category\Grp\EpiMono.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.Algebra.Category.Grp.EquivalenceGroupAddGroup
import Mathlib.GroupTheory.QuotientGroup
import Mathlib.CategoryTheory.ConcreteCategory.EpiMono
import Mathli... |
Algebra\Category\Grp\EquivalenceGroupAddGroup.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.Algebra.Category.Grp.Basic
import Mathlib.Algebra.Group.Equiv.TypeTags
/-!
# Equivalence between `Group` and `AddGroup`
This file contains two equivalenc... |
Algebra\Category\Grp\FilteredColimits.lean | /-
Copyright (c) 2021 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
import Mathlib.Algebra.Category.Grp.Basic
import Mathlib.Algebra.Category.MonCat.FilteredColimits
/-!
# The forgetful functor from (commutative) (additive) groups ... |
Algebra\Category\Grp\ForgetCorepresentable.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.Grp.Basic
import Mathlib.Algebra.Group.ULift
import Mathlib.CategoryTheory.Yoneda
/-!
# The forget functor is corepresentable
It is shown that... |
Algebra\Category\Grp\Images.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Algebra.Category.Grp.Abelian
import Mathlib.CategoryTheory.Limits.Shapes.Images
/-!
# The category of commutative additive groups has images.
Note th... |
Algebra\Category\Grp\Injective.lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import Mathlib.Algebra.Category.Grp.ZModuleEquivalence
import Mathlib.Algebra.EuclideanDomain.Int
import Mathlib.Algebra.Module.Injective
import Mathlib.RingTheory.Princi... |
Algebra\Category\Grp\Kernels.lean | /-
Copyright (c) 2023 Moritz Firsching. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata, Moritz Firsching, Nikolas Kuhn
-/
import Mathlib.Algebra.Category.Grp.EpiMono
import Mathlib.Algebra.Category.Grp.Preadditive
import Mathlib.CategoryTheory.... |
Algebra\Category\Grp\Limits.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Algebra.Category.MonCat.Limits
import Mathlib.Algebra.Category.Grp.ForgetCorepresentable
import Mathlib.Algebra.Category.Grp.Preadditive
import Mathlib... |
Algebra\Category\Grp\Preadditive.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.Algebra.Category.Grp.Basic
import Mathlib.CategoryTheory.Preadditive.Basic
/-!
# The category of additive commutative groups is preadditive.
-/
open Ca... |
Algebra\Category\Grp\Subobject.lean | /-
Copyright (c) 2021 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.Algebra.Category.Grp.ZModuleEquivalence
import Mathlib.Algebra.Category.ModuleCat.Subobject
/-!
# The category of abelian groups is well-powered
-/
op... |
Algebra\Category\Grp\Zero.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Algebra.Category.Grp.Basic
import Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects
/-!
# The category of (commutative) (additive) groups has a zero ob... |
Algebra\Category\Grp\ZModuleEquivalence.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Algebra.Category.ModuleCat.Basic
/-!
The forgetful functor from ℤ-modules to additive commutative groups is
an equivalence of categories.
TODO:
eithe... |
Algebra\Category\HopfAlgebraCat\Basic.lean | /-
Copyright (c) 2024 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.Algebra.Category.BialgebraCat.Basic
import Mathlib.RingTheory.HopfAlgebra
/-!
# The category of Hopf algebras over a commutative ring
We introd... |
Algebra\Category\ModuleCat\Abelian.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.LinearAlgebra.Isomorphisms
import Mathlib.Algebra.Category.ModuleCat.Kernels
import Mathlib.Algebra.Category.ModuleCat.Limits
import Mathlib.CategoryTheo... |
Algebra\Category\ModuleCat\Adjunctions.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johan Commelin
-/
import Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic
import Mathlib.CategoryTheory.Monoidal.Functorial
import Mathlib.CategoryTheory.Monoidal.Type... |
Algebra\Category\ModuleCat\Algebra.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.Algebra.Algebra.RestrictScalars
import Mathlib.CategoryTheory.Linear.Basic
import Mathlib.Algebra.Category.ModuleCat.Basic
/-!
# Additional typeclass ... |
Algebra\Category\ModuleCat\Basic.lean | /-
Copyright (c) 2019 Robert A. Spencer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert A. Spencer, Markus Himmel
-/
import Mathlib.Algebra.Category.Grp.Preadditive
import Mathlib.Algebra.Module.Equiv.Basic
import Mathlib.Algebra.PUnitInstances.Module
import Mat... |
Algebra\Category\ModuleCat\Biproducts.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.Algebra.Group.Pi.Lemmas
import Mathlib.CategoryTheory.Limits.Shapes.Biproducts
import Mathlib.Algebra.Category.ModuleCat.Abelian
import Mathlib.Algebra... |
Algebra\Category\ModuleCat\ChangeOfRings.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.Algebra.Category.ModuleCat.EpiMono
import Mathlib.Algebra.Category.ModuleCat.Colimits
import Mathlib.Algebra.Category.ModuleCat.Limits
import Mathlib.RingT... |
Algebra\Category\ModuleCat\Colimits.lean | /-
Copyright (c) 2019 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.Category.ModuleCat.Basic
import Mathlib.CategoryTheory.ConcreteCategory.Elementwise
import Mathlib.Algebra.Category.Grp.Colimits
/-... |
Algebra\Category\ModuleCat\EpiMono.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.LinearAlgebra.Quotient
import Mathlib.Algebra.Category.ModuleCat.Basic
import Mathlib.CategoryTheory.ConcreteCategory.EpiMono
/-!
# Monomorphisms in `... |
Algebra\Category\ModuleCat\FilteredColimits.lean | /-
Copyright (c) 2021 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
import Mathlib.Algebra.Category.Grp.FilteredColimits
import Mathlib.Algebra.Category.ModuleCat.Basic
/-!
# The forgetful functor from `R`-modules preserves filtere... |
Algebra\Category\ModuleCat\Free.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.LinearAlgebra.Dimension.Free
import Mathlib.Algebra.Homology.ShortComplex.ModuleCat
/-!
# Exact sequences with free modules
This file proves resu... |
Algebra\Category\ModuleCat\Images.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.Algebra.Category.ModuleCat.Abelian
import Mathlib.CategoryTheory.Limits.Shapes.Images
/-!
# The category of R-modules has images.
Note that we don't ... |
Algebra\Category\ModuleCat\Injective.lean | /-
Copyright (c) 2023 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import Mathlib.Algebra.Category.ModuleCat.ChangeOfRings
import Mathlib.Algebra.Category.Grp.EnoughInjectives
import Mathlib.Algebra.Category.Grp.ZModuleEquivalence
import... |
Algebra\Category\ModuleCat\Kernels.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.Algebra.Category.ModuleCat.EpiMono
import Mathlib.CategoryTheory.ConcreteCategory.Elementwise
/-!
# The concrete (co)kernels in the category of modules ... |
Algebra\Category\ModuleCat\Limits.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Algebra.Category.ModuleCat.Basic
import Mathlib.Algebra.Category.Grp.Limits
import Mathlib.Algebra.DirectLimit
/-!
# The category of R-modules has all... |
Algebra\Category\ModuleCat\Presheaf.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.Algebra.Category.ModuleCat.ChangeOfRings
import Mathlib.Algebra.Category.Ring.Basic
/-!
# Presheaves of modules over a presheaf of rings.
We give a h... |
Algebra\Category\ModuleCat\Products.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.Algebra.Category.ModuleCat.Basic
import Mathlib.LinearAlgebra.Pi
import Mathlib.Tactic.CategoryTheory.Elementwise
/-!
# The concrete products in the c... |
Algebra\Category\ModuleCat\Projective.lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
-/
import Mathlib.Algebra.Category.ModuleCat.EpiMono
import Mathlib.Algebra.Module.Projective
import Mathlib.CategoryTheory.Preadditive.Projective
import M... |
Algebra\Category\ModuleCat\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.Presheaf
import Mathlib.Algebra.Category.ModuleCat.Limits
import Mathlib.CategoryTheory.Sites.LocallyBijective
import Mathlib.Categor... |
Algebra\Category\ModuleCat\Simple.lean | /-
Copyright (c) 2022 Pierre-Alexandre Bazin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pierre-Alexandre Bazin, Scott Morrison
-/
import Mathlib.CategoryTheory.Simple
import Mathlib.Algebra.Category.ModuleCat.Subobject
import Mathlib.Algebra.Category.ModuleCat.Alg... |
Algebra\Category\ModuleCat\Subobject.lean | /-
Copyright (c) 2021 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.Algebra.Category.ModuleCat.EpiMono
import Mathlib.Algebra.Category.ModuleCat.Kernels
import Mathlib.CategoryTheory.Subobject.WellPowered
import Mathlib.C... |
Algebra\Category\ModuleCat\Tannaka.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.Algebra.Category.ModuleCat.Basic
import Mathlib.LinearAlgebra.Span
/-!
# Tannaka duality for rings
A ring `R` is equivalent to
the endomorphisms of t... |
Algebra\Category\ModuleCat\Differentials\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.Category.ModuleCat.ChangeOfRings
import Mathlib.Algebra.Category.Ring.Basic
import Mathlib.RingTheory.Kaehler.Basic
/-!
# The differentials of a morphis... |
Algebra\Category\ModuleCat\Differentials\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.Algebra.Category.ModuleCat.Differentials.Basic
/-!
# The presheaf of differentials of a presheaf of modules
... |
Algebra\Category\ModuleCat\Monoidal\Basic.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Scott Morrison, Jakob von Raumer
-/
import Mathlib.Algebra.Category.ModuleCat.Basic
import Mathlib.LinearAlgebra.TensorProduct.Basic
import Mathlib.CategoryTheory.Monoid... |
Algebra\Category\ModuleCat\Monoidal\Closed.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Scott Morrison, Jakob von Raumer
-/
import Mathlib.CategoryTheory.Closed.Monoidal
import Mathlib.CategoryTheory.Linear.Yoneda
import Mathlib.Algebra.Category.ModuleCat.M... |
Algebra\Category\ModuleCat\Monoidal\Symmetric.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Scott Morrison, Jakob von Raumer
-/
import Mathlib.CategoryTheory.Monoidal.Braided.Basic
import Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic
/-!
# The symmetric mo... |
Algebra\Category\ModuleCat\Presheaf\Abelian.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.Colimits
import Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits
import Mathlib.Algebra.Category.ModuleCat.Abelian
import M... |
Algebra\Category\ModuleCat\Presheaf\ChangeOfRings.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.ChangeOfRings
import Mathlib.Algebra.Category.ModuleCat.Presheaf
/-!
# Change of presheaf of rings
In this file, we define the restr... |
Algebra\Category\ModuleCat\Presheaf\Colimits.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.Algebra.Category.ModuleCat.Colimits
/-! # Colimits in categories of presheaves of modules
In this file, it i... |
Algebra\Category\ModuleCat\Presheaf\Limits.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.Algebra.Category.ModuleCat.ChangeOfRings
import Mathlib.CategoryTheory.Limits.Preserves.Limits
import Mathlib.... |
Algebra\Category\ModuleCat\Presheaf\Pushforward.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.ChangeOfRings
/-!
# Pushforward of presheaves of modules
If `F : C ⥤ D`, the precomposition `F.op ⋙ _` induces a functor fr... |
Algebra\Category\ModuleCat\Presheaf\Sheafification.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.Abelian
import Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify
import Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits... |
Algebra\Category\ModuleCat\Presheaf\Sheafify.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.ChangeOfRings
import Mathlib.CategoryTheory.Sites.LocallySurjective
/-!
# The associated sheaf of a presheaf of modules
In thi... |
Algebra\Category\ModuleCat\Sheaf\Abelian.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.Sheafification
import Mathlib.CategoryTheory.Abelian.Transfer
/-!
# The category of sheaves of modules is abelian
In this f... |
Algebra\Category\ModuleCat\Sheaf\ChangeOfRings.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
import Mathlib.Algebra.Category.ModuleCat.Presheaf.ChangeOfRings
import Mathlib.CategoryTheory.Sites.LocallySurjective
/-!
# Ch... |
Algebra\Category\ModuleCat\Sheaf\Colimits.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.Sheafification
/-!
# Colimits in categories of sheaves of modules
In this file, we show that colimits of shape `J` exists i... |
Algebra\Category\ModuleCat\Sheaf\Free.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.Colimits
import Mathlib.Algebra.Category.ModuleCat.Sheaf.Colimits
/-!
# Free sheaves of modules
In this file, we construct ... |
Algebra\Category\ModuleCat\Sheaf\Generators.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.Free
import Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous
import Mathlib.CategoryTheory.Sites.CoversTop
/-!
#... |
Algebra\Category\ModuleCat\Sheaf\Limits.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.Limits
import Mathlib.Algebra.Category.ModuleCat.Sheaf
import Mathlib.CategoryTheory.Sites.Limits
/-! # Limits in categories... |
Algebra\Category\ModuleCat\Sheaf\PushforwardContinuous.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.Pushforward
import Mathlib.Algebra.Category.ModuleCat.Sheaf
import Mathlib.CategoryTheory.Sites.Over
/-!
# Pushforward of sh... |
Algebra\Category\ModuleCat\Sheaf\Quasicoherent.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.Generators
/-!
# Quasicoherent sheaves
A sheaf of modules is quasi-coherent if it admits locally a presentation as the
cokerne... |
Algebra\Category\MonCat\Adjunctions.lean | /-
Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
import Mathlib.Algebra.Category.MonCat.Basic
import Mathlib.Algebra.Category.Semigrp.Basic
import Mathlib.Algebra.Group.WithOne.Basic
import Mathlib.Algebra.F... |
Algebra\Category\MonCat\Basic.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.ConcreteCategory.BundledHom
import Mathlib.Algebra.PUnitInstances.Algebra
import Mathlib.Algebra.Group.ULift
import Mathlib.CategoryTheo... |
Algebra\Category\MonCat\Colimits.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Algebra.Category.MonCat.Basic
import Mathlib.CategoryTheory.Limits.HasLimits
import Mathlib.CategoryTheory.ConcreteCategory.Elementwise
/-!
# The cate... |
Algebra\Category\MonCat\FilteredColimits.lean | /-
Copyright (c) 2021 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
import Mathlib.Algebra.Category.MonCat.Limits
import Mathlib.CategoryTheory.Limits.Preserves.Filtered
import Mathlib.CategoryTheory.ConcreteCategory.Elementwise
imp... |
Algebra\Category\MonCat\Limits.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Algebra.Category.MonCat.Basic
import Mathlib.Algebra.Group.Pi.Lemmas
import Mathlib.Algebra.Group.Submonoid.Operations
import Mathlib.CategoryTheory.Li... |
Algebra\Category\Ring\Adjunctions.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johannes Hölzl
-/
import Mathlib.Algebra.Category.Ring.Basic
import Mathlib.Algebra.MvPolynomial.CommRing
/-!
Multivariable polynomials on a type is the left adjoint o... |
Algebra\Category\Ring\Basic.lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.Algebra.Category.Grp.Basic
import Mathlib.CategoryTheory.ConcreteCategory.ReflectsIso
import Mathlib.Algebra.Ring.Equi... |
Algebra\Category\Ring\Colimits.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Algebra.Category.Ring.Basic
import Mathlib.CategoryTheory.Limits.HasLimits
/-!
# The category of commutative rings has all colimits.
This file uses a... |
Algebra\Category\Ring\Constructions.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.RingTheory.TensorProduct.Basic
import Mathlib.Algebra.Category.Ring.Limits
import Mathlib.Algebra.Category.Ring.Instances
import Mathlib.CategoryTheory.Limit... |
Algebra\Category\Ring\FilteredColimits.lean | /-
Copyright (c) 2021 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
import Mathlib.Algebra.Category.Ring.Basic
import Mathlib.Algebra.Category.Grp.FilteredColimits
/-!
# The forgetful functor from (commutative) (semi-) rings preser... |
Algebra\Category\Ring\Instances.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.Algebra.Category.Ring.Basic
import Mathlib.RingTheory.Localization.Away.Basic
import Mathlib.RingTheory.LocalRing.RingHom.Basic
/-!
# Ring-theoretic results... |
Algebra\Category\Ring\Limits.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Algebra.Ring.Pi
import Mathlib.Algebra.Category.Ring.Basic
import Mathlib.Algebra.Category.Grp.Limits
import Mathlib.Algebra.Ring.Subring.Basic
/-!
# ... |
Algebra\Category\Semigrp\Basic.lean | /-
Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
import Mathlib.Algebra.PEmptyInstances
import Mathlib.Algebra.Group.Equiv.Basic
import Mathlib.CategoryTheory.ConcreteCategory.BundledHom
import Mathlib.Categ... |
Algebra\CharP\Algebra.lean | /-
Copyright (c) 2021 Jon Eugster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jon Eugster, Eric Wieser
-/
import Mathlib.Algebra.CharP.Defs
import Mathlib.Algebra.FreeAlgebra
import Mathlib.RingTheory.Localization.FractionRing
/-!
# Characteristics of algebras
In... |
Algebra\CharP\Basic.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Joey van Langen, Casper Putz
-/
import Mathlib.Algebra.CharP.Defs
import Mathlib.Data.Nat.Multiplicity
import Mathlib.Data.Nat.Choose.Sum
/-!
# Characteristic of semirings
-/
a... |
Algebra\CharP\CharAndCard.lean | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import Mathlib.Algebra.CharP.Basic
import Mathlib.GroupTheory.Perm.Cycle.Type
import Mathlib.RingTheory.Coprime.Lemmas
/-!
# Characteristic and cardinality
We prove s... |
Algebra\CharP\Defs.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Joey van Langen, Casper Putz
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.ULift
import Mathlib.Data.Int.ModEq
import ... |
Algebra\CharP\ExpChar.lean | /-
Copyright (c) 2021 Jakob Scholbach. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob Scholbach
-/
import Mathlib.Algebra.CharP.Basic
import Mathlib.Algebra.CharP.Algebra
import Mathlib.Data.Nat.Prime.Defs
/-!
# Exponential characteristic
This file defines the ... |
Algebra\CharP\IntermediateField.lean | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
import Mathlib.FieldTheory.IntermediateField
import Mathlib.Algebra.CharP.ExpChar
/-!
# Characteristic of intermediate fields
This file contains some convenient instances for dete... |
Algebra\CharP\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.CharP.Defs
/-!
# Invertibility of elements given a characteristic
This file includes some instances of `Invertible` for specific numbers in
charact... |
Algebra\CharP\LocalRing.lean | /-
Copyright (c) 2022 Jon Eugster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jon Eugster
-/
import Mathlib.Algebra.CharP.Basic
import Mathlib.Algebra.IsPrimePow
import Mathlib.Data.Nat.Factorization.Basic
import Mathlib.RingTheory.LocalRing.ResidueField.Defs
/-!
... |
Algebra\CharP\MixedCharZero.lean | /-
Copyright (c) 2022 Jon Eugster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jon Eugster
-/
import Mathlib.Algebra.CharP.LocalRing
import Mathlib.RingTheory.Ideal.Quotient
import Mathlib.Tactic.FieldSimp
/-!
# Equal and mixed characteristic
In commutative algebr... |
Algebra\CharP\Pi.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.CharP.Defs
import Mathlib.Algebra.Ring.Pi
/-!
# Characteristic of semirings of functions
-/
universe u v
namespace CharP
instance pi (ι : Type u) [h... |
Algebra\CharP\Quotient.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Eric Wieser
-/
import Mathlib.GroupTheory.OrderOfElement
import Mathlib.RingTheory.Ideal.Maps
import Mathlib.RingTheory.Ideal.Quotient
/-!
# Characteristic of quotients rings
-/... |
Algebra\CharP\Reduced.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Joey van Langen, Casper Putz
-/
import Mathlib.Algebra.CharP.ExpChar
import Mathlib.RingTheory.Nilpotent.Defs
/-!
# Results about characteristic p reduced rings
-/
open Finset... |
Algebra\CharP\Subring.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.CharP.Defs
import Mathlib.Algebra.Ring.Subring.Basic
/-!
# Characteristic of subrings
-/
universe u v
namespace CharP
instance subsemiring (R : Type... |
Algebra\CharP\Two.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.CharP.ExpChar
import Mathlib.GroupTheory.OrderOfElement
/-!
# Lemmas about rings of characteristic two
This file contains results about `CharP R 2`... |
Algebra\CharZero\Defs.lean | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.Int.Cast.Defs
import Mathlib.Tactic.Cases
import Mathlib.Algebra.NeZero
import Mathlib.Logic.Function.Basic
/-!
# Characteristic zero
A ring `R... |
Algebra\CharZero\Infinite.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.CharZero.Defs
import Mathlib.Data.Fintype.Card
/-! # A characteristic-zero semiring is infinite -/
open Set
variable (M : Type*) [AddMonoid... |
Algebra\CharZero\Lemmas.lean | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Group.Support
import Mathlib.Algebra.Order.Monoid.Unbundled.Pow
import Mathlib.Algebra.Order.Monoid.Unbundle... |
Algebra\CharZero\Quotient.lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.GroupTheory.QuotientGroup
/-!
# Lemmas about quotients in characteristic zero
-/
variable {R : Type*} [DivisionRing R] [CharZero R] {p : R}
namespace Add... |
Algebra\ContinuedFractions\Basic.lean | /-
Copyright (c) 2019 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import Mathlib.Data.Seq.Seq
import Mathlib.Algebra.Field.Defs
/-!
# Basic Definitions/Theorems for Continued Fractions
## Summary
We define generalised, simple... |
Algebra\ContinuedFractions\ContinuantsRecurrence.lean | /-
Copyright (c) 2019 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import Mathlib.Algebra.ContinuedFractions.Translations
/-!
# Recurrence Lemmas for the Continuants (`conts`) Function of Continued Fractions
## Summary
Given a... |
Algebra\ContinuedFractions\ConvergentsEquiv.lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import Mathlib.Algebra.ContinuedFractions.ContinuantsRecurrence
import Mathlib.Algebra.ContinuedFractions.TerminatedStable
import Mathlib.Tactic.FieldSimp
import ... |
Algebra\ContinuedFractions\Determinant.lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import Mathlib.Algebra.ContinuedFractions.ContinuantsRecurrence
import Mathlib.Algebra.ContinuedFractions.TerminatedStable
import Mathlib.Tactic.Ring
/-!
# Deter... |
Algebra\ContinuedFractions\TerminatedStable.lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import Mathlib.Algebra.ContinuedFractions.Translations
/-!
# Stabilisation of gcf Computations Under Termination
## Summary
We show that the continuants and co... |
Algebra\ContinuedFractions\Translations.lean | /-
Copyright (c) 2019 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import Mathlib.Algebra.ContinuedFractions.Basic
import Mathlib.Algebra.GroupWithZero.Basic
/-!
# Basic Translation Lemmas Between Functions Defined for Continued... |
Algebra\ContinuedFractions\Computation\ApproximationCorollaries.lean | /-
Copyright (c) 2021 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import Mathlib.Algebra.ContinuedFractions.Computation.Approximations
import Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv
import Mathlib.Algebra.Order.Archi... |
Algebra\ContinuedFractions\Computation\Approximations.lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import Mathlib.Algebra.ContinuedFractions.Determinant
import Mathlib.Algebra.ContinuedFractions.Computation.CorrectnessTerminating
import Mathlib.Algebra.Order.Gr... |
Algebra\ContinuedFractions\Computation\Basic.lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import Mathlib.Algebra.Order.Floor
import Mathlib.Algebra.ContinuedFractions.Basic
/-!
# Computable Continued Fractions
## Summary
We formalise the standard co... |
Algebra\ContinuedFractions\Computation\CorrectnessTerminating.lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import Mathlib.Algebra.ContinuedFractions.Computation.Translations
import Mathlib.Algebra.ContinuedFractions.TerminatedStable
import Mathlib.Algebra.ContinuedFrac... |
Algebra\ContinuedFractions\Computation\TerminatesIffRat.lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import Mathlib.Algebra.ContinuedFractions.Computation.Approximations
import Mathlib.Algebra.ContinuedFractions.Computation.CorrectnessTerminating
import Mathlib.D... |
Algebra\ContinuedFractions\Computation\Translations.lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import Mathlib.Algebra.ContinuedFractions.Computation.Basic
import Mathlib.Algebra.ContinuedFractions.Translations
/-!
# Basic Translation Lemmas Between Structu... |
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