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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...