path stringlengths 11 71 | content stringlengths 75 124k |
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CategoryTheory\Sites\Over.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Sites.CoverLifting
import Mathlib.CategoryTheory.Sites.CoverPreserving
/-! Localization
In this file, given a Grothendieck topology `J` on a cat... |
CategoryTheory\Sites\Plus.lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import Mathlib.CategoryTheory.Sites.Sheaf
/-!
# The plus construction for presheaves.
This file contains the construction of `P⁺`, for a presheaf `P : Cᵒᵖ ⥤ D`
where `C` i... |
CategoryTheory\Sites\Preserves.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Sites.Equ... |
CategoryTheory\Sites\PreservesLocallyBijective.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.Sites.DenseSubsite
import Mathlib.CategoryTheory.Sites.LocallySurjective
/-!
# Preserving and reflecting local injectivity and surj... |
CategoryTheory\Sites\PreservesSheafification.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Sites.Localization
import Mathlib.CategoryTheory.Sites.CompatibleSheafification
import Mathlib.CategoryTheory.Sites.Whiskering
import Mathlib.Cate... |
CategoryTheory\Sites\Pretopology.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.CategoryTheory.Sites.Grothendieck
/-!
# Grothendieck pretopologies
Definition and lemmas about Grothendieck pretopologies.
A Grothendieck pretopology for... |
CategoryTheory\Sites\Pullback.lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.CategoryTheory.Adjunction.Restrict
import Mathlib.CategoryTheory.Functor.Flat
import Mathlib.CategoryTheory.Sites.Continuous
import Mathlib.CategoryTheory.Si... |
CategoryTheory\Sites\Sheaf.lean | /-
Copyright (c) 2020 Kevin Buzzard, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products
import Mathl... |
CategoryTheory\Sites\SheafHom.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Sites.Over
/-! Internal hom of sheaves
In this file, given two sheaves `F` and `G` on a site `(C, J)` with values
in a category `A`, we define ... |
CategoryTheory\Sites\Sheafification.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.Adjunction.Unique
import Mathlib.CategoryTheory.Adjunction.FullyFaithful
import Mathlib.CategoryTheory.Sites.Sheaf
import Mathlib.Ca... |
CategoryTheory\Sites\SheafOfTypes.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.CategoryTheory.Sites.Pretopology
import Mathlib.CategoryTheory.Sites.IsSheafFor
/-!
# Sheaves of types on a Grothendieck topology
Defines the notion of a... |
CategoryTheory\Sites\Sieves.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, E. W. Ayers
-/
import Mathlib.CategoryTheory.Comma.Over
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
import Mathlib.CategoryTheory.Yoneda
import Mathlib... |
CategoryTheory\Sites\Spaces.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.CategoryTheory.Sites.Grothendieck
import Mathlib.CategoryTheory.Sites.Pretopology
import Mathlib.CategoryTheory.Limits.Lattice
import Mathlib.Topology.Sets... |
CategoryTheory\Sites\Subsheaf.lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.CategoryTheory.Elementwise
import Mathlib.CategoryTheory.Adjunction.Evaluation
import Mathlib.Tactic.CategoryTheory.Elementwise
import Mathlib.CategoryTheory... |
CategoryTheory\Sites\Types.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.CategoryTheory.Sites.Canonical
/-!
# Grothendieck Topology and Sheaves on the Category of Types
In this file we define a Grothendieck topology on the category ... |
CategoryTheory\Sites\Whiskering.lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import Mathlib.CategoryTheory.Sites.Sheaf
/-!
In this file we construct the functor `Sheaf J A ⥤ Sheaf J B` between sheaf categories
obtained by composition with a functor ... |
CategoryTheory\Sites\Coherent\Basic.lean | /-
Copyright (c) 2023 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Dagur Asgeirsson, Filippo A. E. Nuccio, Riccardo Brasca
-/
import Mathlib.CategoryTheory.Extensive
import Mathlib.CategoryTheory.Sites.Coverage
import Mathlib.CategoryTheory.Ef... |
CategoryTheory\Sites\Coherent\CoherentSheaves.lean | /-
Copyright (c) 2023 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import Mathlib.CategoryTheory.Sites.Canonical
import Mathlib.CategoryTheory.Sites.Coherent.Basic
import Mathlib.CategoryTheory.Sites.EffectiveEpimorphic
/-!
# Sheaves for th... |
CategoryTheory\Sites\Coherent\CoherentTopology.lean | /-
Copyright (c) 2023 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Nick Kuhn
-/
import Mathlib.CategoryTheory.Sites.Coherent.CoherentSheaves
/-!
# Description of the covering sieves of the coherent topology
This file characterises the coveri... |
CategoryTheory\Sites\Coherent\Comparison.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.Sites.Coherent.Basic
import Mathlib.CategoryTheory.EffectiveEpi.Comp
import Mathlib.CategoryTheory.EffectiveEpi.Extensive
/-!
# Con... |
CategoryTheory\Sites\Coherent\Equivalence.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.Sites.Coherent.SheafComparison
import Mathlib.CategoryTheory.Sites.Equivalence
/-!
# Coherence and equivalence of categories
This ... |
CategoryTheory\Sites\Coherent\ExtensiveSheaves.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Filippo A. E. Nuccio, Riccardo Brasca
-/
import Mathlib.CategoryTheory.Limits.Preserves.Finite
import Mathlib.CategoryTheory.Sites.Canonical
import Mathlib.Category... |
CategoryTheory\Sites\Coherent\ExtensiveTopology.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.Sites.Coherent.Basic
/-!
# Description of the covering sieves of the extensive topology
This file characterises the covering sieve... |
CategoryTheory\Sites\Coherent\LocallySurjective.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.Sites.Coherent.ExtensiveTopology
import Mathlib.CategoryTheory.Sites.Coherent.SheafComparison
import Mathlib.CategoryTheory.Sites.Lo... |
CategoryTheory\Sites\Coherent\ReflectsPrecoherent.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.EffectiveEpi.Enough
import Mathlib.CategoryTheory.EffectiveEpi.Preserves
import Mathlib.CategoryTheory.Sites.Coherent.CoherentTopolo... |
CategoryTheory\Sites\Coherent\ReflectsPreregular.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.EffectiveEpi.Enough
import Mathlib.CategoryTheory.EffectiveEpi.Preserves
import Mathlib.CategoryTheory.Sites.Coherent.RegularTopolog... |
CategoryTheory\Sites\Coherent\RegularSheaves.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Filippo A. E. Nuccio, Riccardo Brasca
-/
import Mathlib.CategoryTheory.EffectiveEpi.Preserves
import Mathlib.CategoryTheory.Limits.Final.ParallelPair
import Mathlib... |
CategoryTheory\Sites\Coherent\RegularTopology.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves
/-!
# Description of the covering sieves of the regular topology
This file characterises the coverin... |
CategoryTheory\Sites\Coherent\SheafComparison.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.Sites.Coherent.Comparison
import Mathlib.CategoryTheory.Sites.Coherent.ExtensiveSheaves
import Mathlib.CategoryTheory.Sites.Coherent... |
CategoryTheory\Sites\NonabelianCohomology\H1.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
/-! The cohomology of a sheaf of groups in degree 1
In this file, we shall define the cohomology in degree 1 of a sheaf
of groups (T... |
CategoryTheory\Sites\SheafCohomology\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.Grp.Abelian
import Mathlib.Algebra.Category.Grp.Adjunctions
import Mathlib.Algebra.Homology.DerivedCategory.Ext
import Mathlib.CategoryTheory.Si... |
CategoryTheory\SmallObject\Construction.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.Products
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
/-!
# Construction for the small object argument
Given a... |
CategoryTheory\SmallObject\Iteration.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.Category.Preorder
import Mathlib.CategoryTheory.Limits.IsLimit
import Mathlib.Order.IsWellOrderLimitElement
/-! # Transfinite iterations of a fun... |
CategoryTheory\Subobject\Basic.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Scott Morrison
-/
import Mathlib.CategoryTheory.Subobject.MonoOver
import Mathlib.CategoryTheory.Skeletal
import Mathlib.CategoryTheory.ConcreteCategory.Basic
import Mathli... |
CategoryTheory\Subobject\Comma.lean | /-
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Subobject.WellPowered
import Mathlib.CategoryTheory.Limits.Preserves.Finite
import Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits
impor... |
CategoryTheory\Subobject\FactorThru.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Scott Morrison
-/
import Mathlib.CategoryTheory.Subobject.Basic
import Mathlib.CategoryTheory.Preadditive.Basic
/-!
# Factoring through subobjects
The predicate `h : P.... |
CategoryTheory\Subobject\Lattice.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Scott Morrison
-/
import Mathlib.CategoryTheory.Functor.Currying
import Mathlib.CategoryTheory.Subobject.FactorThru
import Mathlib.CategoryTheory.Subobject.WellPowered
/... |
CategoryTheory\Subobject\Limits.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Scott Morrison
-/
import Mathlib.CategoryTheory.Subobject.Lattice
/-!
# Specific subobjects
We define `equalizerSubobject`, `kernelSubobject` and `imageSubobject`, whic... |
CategoryTheory\Subobject\MonoOver.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Scott Morrison
-/
import Mathlib.CategoryTheory.Adjunction.Over
import Mathlib.CategoryTheory.Adjunction.Reflective
import Mathlib.CategoryTheory.Adjunction.Restrict
import... |
CategoryTheory\Subobject\Types.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.WellPowered
import Mathlib.CategoryTheory.Types
import Mathlib.Data.Set.Subsingleton
/-!
# `Type u` is well-powered
By build... |
CategoryTheory\Subobject\WellPowered.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.Basic
import Mathlib.CategoryTheory.EssentiallySmall
/-!
# Well-powered categories
A category `(C : Type u) [Category.{v} C]... |
CategoryTheory\Sums\Associator.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.CategoryTheory.Sums.Basic
/-!
# Associator for binary disjoint union of categories.
The associator functor `((C ⊕ D) ⊕ E) ⥤ (C ⊕ (D ⊕ E))` and its in... |
CategoryTheory\Sums\Basic.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.CategoryTheory.EqToHom
/-!
# Binary disjoint unions of categories
We define the category instance on `C ⊕ D` when `C` and `D` are categories.
We def... |
CategoryTheory\Triangulated\Basic.lean | /-
Copyright (c) 2021 Luke Kershaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Luke Kershaw
-/
import Mathlib.CategoryTheory.Adjunction.Limits
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products
import Mathlib.CategoryTheory.Limits.Shapes.Biproducts
impo... |
CategoryTheory\Triangulated\Functor.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.Triangulated.Triangulated
import Mathlib.CategoryTheory.ComposableArrows
import Mathlib.CategoryTheory.Shift.CommShift
/-!
# Triangulated functor... |
CategoryTheory\Triangulated\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.ShortComplex.Exact
import Mathlib.CategoryTheory.Shift.ShiftSequence
import Mathlib.CategoryTheory.Triangulated.Functor
import Mathlib.CategoryT... |
CategoryTheory\Triangulated\Opposite.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Shift.Opposite
import Mathlib.CategoryTheory.Shift.Pullback
import Mathlib.CategoryTheory.Triangulated.HomologicalFunctor
import Mathlib.Tactic.Li... |
CategoryTheory\Triangulated\Pretriangulated.lean | /-
Copyright (c) 2021 Luke Kershaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Luke Kershaw, Joël Riou
-/
import Mathlib.Algebra.Homology.ShortComplex.Basic
import Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts
import Mathlib.CategoryThe... |
CategoryTheory\Triangulated\Rotate.lean | /-
Copyright (c) 2021 Luke Kershaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Luke Kershaw
-/
import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
import Mathlib.CategoryTheory.Triangulated.Basic
/-!
# Rotate
This file adds the ability to rotate triangles a... |
CategoryTheory\Triangulated\Subcategory.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.ClosedUnderIsomorphisms
import Mathlib.CategoryTheory.Localization.CalculusOfFractions
import Mathlib.CategoryTheory.Localization.Triangulated
imp... |
CategoryTheory\Triangulated\TriangleShift.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.LinearFunctor
import Mathlib.CategoryTheory.Triangulated.Rotate
import Mathlib.Algebra.Ring.NegOnePow
/-!
# The shift on the category of t... |
CategoryTheory\Triangulated\Triangulated.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.Triangulated.Pretriangulated
/-!
# Triangulated Categories
This file contains the definition of triangulated categories, which are
pretriangulat... |
CategoryTheory\Triangulated\Yoneda.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Homology.ShortComplex.Ab
import Mathlib.CategoryTheory.Preadditive.Yoneda.Basic
import Mathlib.CategoryTheory.Triangulated.HomologicalFunctor
import Math... |
CategoryTheory\Triangulated\TStructure\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.CategoryTheory.Shift.Predicate
import Mathlib.CategoryTheory.Triangulated.Pretriangulated
/-!
# t-structures on triangulated categories
This files introduces t... |
Combinatorics\Colex.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Alena Gusakov, Yaël Dillies
-/
import Mathlib.Algebra.GeomSum
import Mathlib.Data.Finset.Slice
import Mathlib.Data.Nat.BitIndices
import Mathlib.Order.SupClosed
/-!
# Cole... |
Combinatorics\Configuration.lean | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Combinatorics.Hall.Basic
import Mathlib.Data.Fintype.BigOperators
import Mathlib.SetTheory.Car... |
Combinatorics\HalesJewett.lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Data.Countable.Small
import Mathlib.Data.Fintype.Option
import Mathlib.Data.Fintype.Pi
import Mathlib.Data.Fin... |
Combinatorics\Hindman.lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import Mathlib.Topology.StoneCech
import Mathlib.Topology.Algebra.Semigroup
import Mathlib.Data.Stream.Init
/-!
# Hindman's theorem on finite sums
We prove Hindman's theore... |
Combinatorics\Pigeonhole.lean | /-
Copyright (c) 2020 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Yury Kudryashov
-/
import Mathlib.Algebra.Module.BigOperators
import Mathlib.Algebra.Module.Defs
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Data.Na... |
Combinatorics\Schnirelmann.lean | /-
Copyright (c) 2023 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta, Doga Can Sertbas
-/
import Mathlib.Algebra.Order.Ring.Abs
import Mathlib.Data.Nat.ModEq
import Mathlib.Data.Nat.Prime.Defs
import Mathlib.Data.Real.Archimedea... |
Combinatorics\Additive\Dissociation.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Algebra.Group.Units.Equiv
import Mathlib.Data.Fintype.Card
import Mathlib.Data.Set.Pointwise.Basic
/-!
# ... |
Combinatorics\Additive\Energy.lean | /-
Copyright (c) 2022 Yaël Dillies, Ella Yu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Ella Yu
-/
import Mathlib.Algebra.Order.BigOperators.Ring.Finset
import Mathlib.Data.Finset.Prod
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.Finset.Pointw... |
Combinatorics\Additive\ErdosGinzburgZiv.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.BigOperators.Ring
import Mathlib.Data.Multiset.Fintype
import Mathlib.FieldTheory.ChevalleyWarning
import Mathlib.RingTheory.UniqueFactorizationDom... |
Combinatorics\Additive\ETransform.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Data.Finset.Pointwise
/-!
# e-transforms
e-transforms are a family of transformations of pairs of finite sets that aim to reduce the size
of the sumset w... |
Combinatorics\Additive\FreimanHom.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.BigOperators.Ring
import Mathlib.Algebra.CharP.Defs
import Mathlib.Algebra.Order.BigOperators.Group.Multiset
import Mathlib.Data.ZMod.Defs
import M... |
Combinatorics\Additive\PluenneckeRuzsa.lean | /-
Copyright (c) 2022 Yaël Dillies, George Shakan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, George Shakan
-/
import Mathlib.Algebra.Order.Ring.Basic
import Mathlib.Combinatorics.Enumerative.DoubleCounting
import Mathlib.Data.Finset.Pointwise
import ... |
Combinatorics\Additive\RuzsaCovering.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Data.Finset.Pointwise
import Mathlib.SetTheory.Cardinal.Finite
/-!
# Ruzsa's covering lemma
This file proves the Ruzsa covering lemma. This says that, fo... |
Combinatorics\Additive\AP\Three\Behrend.lean | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Analysis.InnerProductSpace.PiL2
import Mathlib.Combinatorics.Additive.AP.Three.Defs
import Mathlib.Combinatorics.Pigeonhole
imp... |
Combinatorics\Additive\AP\Three\Defs.lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Algebra.Order.Interval.Finset
import Mathlib.Combinatorics.Additive.FreimanHom
import Mathlib.Data.Set.Pointwise.SMul
import Ma... |
Combinatorics\Additive\Corner\Defs.lean | /-
Copyright (c) 2024 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Combinatorics.Additive.FreimanHom
/-!
# Corners
This file defines corners, namely triples of the form `(x, y), (x, y + d), (x + d, y)`, and the
property ... |
Combinatorics\Additive\Corner\Roth.lean | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Combinatorics.Additive.AP.Three.Defs
import Mathlib.Combinatorics.Additive.Corner.Defs
import Mathlib.Combinatorics.SimpleGraph... |
Combinatorics\Derangements\Basic.lean | /-
Copyright (c) 2021 Henry Swanson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henry Swanson
-/
import Mathlib.Dynamics.FixedPoints.Basic
import Mathlib.GroupTheory.Perm.Option
import Mathlib.Logic.Equiv.Defs
import Mathlib.Logic.Equiv.Option
/-!
# Derangements o... |
Combinatorics\Derangements\Exponential.lean | /-
Copyright (c) 2021 Henry Swanson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henry Swanson, Patrick Massot
-/
import Mathlib.Analysis.SpecialFunctions.Exponential
import Mathlib.Combinatorics.Derangements.Finite
import Mathlib.Order.Filter.Basic
/-!
# Derangeme... |
Combinatorics\Derangements\Finite.lean | /-
Copyright (c) 2021 Henry Swanson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henry Swanson
-/
import Mathlib.Algebra.BigOperators.Ring
import Mathlib.Combinatorics.Derangements.Basic
import Mathlib.Data.Fintype.BigOperators
import Mathlib.Tactic.Ring
/-!
# Dera... |
Combinatorics\Enumerative\Catalan.lean | /-
Copyright (c) 2022 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Algebra.BigOperators.NatAntidiagonal
import Mathlib.Algebra.CharZero.Lemmas
import Mathlib.Data.Finset.... |
Combinatorics\Enumerative\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
-/
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Data.Finset.Sort
import Mathlib.Data.Set.Subsingle... |
Combinatorics\Enumerative\DoubleCounting.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Data.Set.Subsingleton
/-!
# Double countings
This file gathers a few double counting arguments.
#... |
Combinatorics\Enumerative\Partition.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.Combinatorics.Enumerative.Composition
import Mathlib.Tactic.ApplyFun
/-!
# Partitions
A partition of a natural number `n` is a way of writing `n` as a su... |
Combinatorics\Hall\Basic.lean | /-
Copyright (c) 2021 Alena Gusakov, Bhavik Mehta, Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alena Gusakov, Bhavik Mehta, Kyle Miller
-/
import Mathlib.Combinatorics.Hall.Finite
import Mathlib.CategoryTheory.CofilteredSystem
import Mathlib.Data.Rel
/... |
Combinatorics\Hall\Finite.lean | /-
Copyright (c) 2021 Alena Gusakov, Bhavik Mehta, Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alena Gusakov, Bhavik Mehta, Kyle Miller
-/
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Set.Finite
/-!
# Hall's Marriage Theorem for finite index t... |
Combinatorics\Optimization\ValuedCSP.lean | /-
Copyright (c) 2023 Martin Dvorak. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Martin Dvorak
-/
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Algebra.Order.BigOperators.Group.Multiset
import Mathlib.Data.Fin.VecNotation
import Mathlib.Data.Matrix.Notation... |
Combinatorics\Quiver\Arborescence.lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import Mathlib.Combinatorics.Quiver.Path
import Mathlib.Combinatorics.Quiver.Subquiver
import Mathlib.Order.WellFounded
/-!
# Arborescences
A quiver `V` is an arborescence ... |
Combinatorics\Quiver\Basic.lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn, Scott Morrison
-/
import Mathlib.Data.Opposite
import Mathlib.Tactic.Cases
/-!
# Quivers
This module defines quivers. A quiver on a type `V` of vertices assigns to every
pair... |
Combinatorics\Quiver\Cast.lean | /-
Copyright (c) 2022 Antoine Labelle, Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle, Rémi Bottinelli
-/
import Mathlib.Combinatorics.Quiver.Basic
import Mathlib.Combinatorics.Quiver.Path
/-!
# Rewriting arrows and paths along vertex... |
Combinatorics\Quiver\ConnectedComponent.lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import Mathlib.Combinatorics.Quiver.Subquiver
import Mathlib.Combinatorics.Quiver.Path
import Mathlib.Combinatorics.Quiver.Symmetric
/-!
## Weakly connected components
For ... |
Combinatorics\Quiver\Covering.lean | /-
Copyright (c) 2022 Antoine Labelle, Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle, Rémi Bottinelli
-/
import Mathlib.Combinatorics.Quiver.Cast
import Mathlib.Combinatorics.Quiver.Symmetric
import Mathlib.Data.Sigma.Basic
import Math... |
Combinatorics\Quiver\Path.lean | /-
Copyright (c) 2021 David Wärn,. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn, Scott Morrison
-/
import Mathlib.Combinatorics.Quiver.Basic
import Mathlib.Logic.Lemmas
/-!
# Paths in quivers
Given a quiver `V`, we define the type of paths from `a : V` t... |
Combinatorics\Quiver\Push.lean | /-
Copyright (c) 2022 Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémi Bottinelli
-/
import Mathlib.Combinatorics.Quiver.Basic
/-!
# Pushing a quiver structure along a map
Given a map `σ : V → W` and a `Quiver` instance on `V`, this files defines... |
Combinatorics\Quiver\SingleObj.lean | /-
Copyright (c) 2023 Antoine Labelle. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle
-/
import Mathlib.Combinatorics.Quiver.Cast
import Mathlib.Combinatorics.Quiver.Symmetric
/-!
# Single-object quiver
Single object quiver with a given arrows type.
... |
Combinatorics\Quiver\Subquiver.lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import Mathlib.Order.Notation
import Mathlib.Combinatorics.Quiver.Basic
/-!
## Wide subquivers
A wide subquiver `H` of a quiver `H` consists of a subset of the edge set `a ... |
Combinatorics\Quiver\Symmetric.lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn, Antoine Labelle, Rémi Bottinelli
-/
import Mathlib.Combinatorics.Quiver.Path
import Mathlib.Combinatorics.Quiver.Push
import Batteries.Data.Sum.Lemmas
/-!
## Symmetric quivers... |
Combinatorics\SetFamily\AhlswedeZhang.lean | /-
Copyright (c) 2023 Yaël Dillies, Vladimir Ivanov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Vladimir Ivanov
-/
import Mathlib.Algebra.BigOperators.Intervals
import Mathlib.Algebra.BigOperators.Ring
import Mathlib.Algebra.Order.BigOperators.Group.F... |
Combinatorics\SetFamily\CauchyDavenport.lean | /-
Copyright (c) 2023 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Combinatorics.Additive.ETransform
import Mathlib.GroupTheory.Order.Min
/-!
# The Cauchy-Davenport theorem
This file proves a ... |
Combinatorics\SetFamily\FourFunctions.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.Order.Pi
import Mathlib.Algebra.Order.Ring.Basic
import Mathlib.Data.Finset.Sups
import Math... |
Combinatorics\SetFamily\HarrisKleitman.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Order.Ring.Nat
import Mathlib.Combinatorics.SetFamily.Compression.Down
import Mathlib.Order.UpperLower.Basic
import Mathlib.Data.Fintype.Powerset
... |
Combinatorics\SetFamily\Intersecting.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Data.Fintype.Card
import Mathlib.Order.UpperLower.Basic
/-!
# Intersecting families
This file defines intersecting families and proves their basic proper... |
Combinatorics\SetFamily\Kleitman.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Combinatorics.SetFamily.HarrisKleitman
import Mathlib.Combinatorics.SetFamily.Intersecting
/-!
# Kleitman's bound on the size of intersecting families
An... |
Combinatorics\SetFamily\LYM.lean | /-
Copyright (c) 2022 Bhavik Mehta, Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Alena Gusakov, Yaël Dillies
-/
import Mathlib.Algebra.BigOperators.Ring
import Mathlib.Algebra.Field.Rat
import Mathlib.Algebra.Order.Field.Basic
import Mathl... |
Combinatorics\SetFamily\Shadow.lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Alena Gusakov, Yaël Dillies
-/
import Mathlib.Data.Finset.Grade
import Mathlib.Data.Finset.Sups
import Mathlib.Logic.Function.Iterate
/-!
# Shadows
This file defines shad... |
Combinatorics\SetFamily\Shatter.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Combinatorics.SetFamily.Compression.Down
import Mathlib.Order.Interval.Finset.Nat
import Mathlib.Order.Upp... |
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