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Theorems · Definition · category theory

AlgebraicTopology.inclusionOfMooreComplexMap

{A : Type u_2} →
  [inst : CategoryTheory.Category.{v_2, u_2} A] →
    [inst_1 : CategoryTheory.Abelian A] →
      (X : CategoryTheory.SimplicialObject A) →
        (AlgebraicTopology.normalizedMooreComplex A).obj X ⟶ (AlgebraicTopology.alternatingFaceMapComplex A).obj X

The inclusion map of the Moore complex in the alternating face map complex

Defined in
Mathlib.AlgebraicTopology.AlternatingFaceMapComplex
Cited by
10 results in Mathlib
Foundations
Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Abelian

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicTopology.DoldKan.homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex · cited by 4DoldKan.homotopyEquivNorm…AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap · cited by 2DoldKan.PInftyToNormalize…AlgebraicTopology.DoldKan.N₁_iso_normalizedMooreComplex_comp_toKaroubi · cited by 2DoldKan.N₁_iso_normalized…AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInfty · cited by 1DoldKan.inclusionOfMooreC…AlgebraicTopology.DoldKan.HigherFacesVanish.inclusionOfMooreComplexMap · cited by 1HigherFacesVanish.inclusi…AlgebraicTopology.inclusionOfMooreComplexMap_f · cited by 1AlgebraicTopology.inclusi…AlgebraicTopology.inclusionOfMooreComplex · cited by 1AlgebraicTopology.inclusi…AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInfty_assoc · cited by 0DoldKan.inclusionOfMooreC…AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap_assoc · cited by 0DoldKan.PInftyToNormalize…AlgebraicTopology.DoldKan.homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex_homotopyInvHomId · cited by 0DoldKan.homotopyEquivNorm…AlgebraicTopology.DoldKan.homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex_hom · cited by 0DoldKan.homotopyEquivNorm…AlgebraicTopology.DoldKan.homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex_homotopyHomInvId · cited by 0DoldKan.homotopyEquivNorm…AlgebraicTopology.inclusionOfMooreComplex_app · cited by 0AlgebraicTopology.inclusi…AlgebraicTopology.DoldKan.splitMonoInclusionOfMooreComplexMap · cited by 0DoldKan.splitMonoInclusio…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objOpposite · cited by 8081OppositeSimplexCategory · cited by 2204SimplexCategoryCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianComplexShape.down · cited by 605ComplexShape.downCategoryTheory.SimplicialObject · cited by 548CategoryTheory.Simplicial…ChainComplex · cited by 350ChainComplexCategoryTheory.Subobject.arrow · cited by 175Subobject.arrowAlgebraicTopology.alternatingFaceMapComplex · cited by 25AlgebraicTopology.alterna…AlgebraicTopology.normalizedMooreComplex · cited by 14AlgebraicTopology.normali…AlgebraicTopology.NormalizedMooreComplex.objX · cited by 13NormalizedMooreComplex.ob…ChainComplex.ofHom · cited by 0ChainComplex.ofHomAlgebraicTopology.inclusionOf…CITED BYCITES

Cites14

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Cited by14

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