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Theorems · Definition · algebraic topology

SSet.chainComplexMap

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasCoproducts C] →
      [inst_2 : CategoryTheory.Preadditive C] → {X Y : SSet} → (X ⟶ Y) → (R : C) → X.chainComplex R ⟶ Y.chainComplex R

The morphism of simplicial chain complexes induces by a morphism of simplicial sets.

Defined in
Mathlib.AlgebraicTopology.SimplicialSet.Homology.Basic
Cited by
8 results in Mathlib
Foundations
Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasCoproductsCategoryTheory.Preadditive

Around this declaration

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

SSet.homologyMap · cited by 9SSet.homologyMapSSet.normalizedChainComplexMap · cited by 5SSet.normalizedChainCompl…SSet.toNormalizedChainComplex_normalizedChainComplexMap · cited by 2SSet.toNormalizedChainCom…SSet.chainComplexMap_PInfty · cited by 1SSet.chainComplexMap_PInf…CategoryTheory.SimplicialObject.Homotopy.sSetChainComplexMap · cited by 1Homotopy.sSetChainComplex…SSet.homologyMap_comp · cited by 1SSet.homologyMap_compSSet.Homotopy.chainComplexMap · cited by 1Homotopy.chainComplexMapSSet.ι_chainComplexMap_f · cited by 1SSet.ι_chainComplexMap_fSSet.ι_chainComplexMap_f_assoc · cited by 1SSet.ι_chainComplexMap_f_…SSet.ι_normalizedChainComplexMap_f · cited by 1SSet.ι_normalizedChainCom…SSet.toNormalizedChainComplex_normalizedChainComplexMap_assoc · cited by 0SSet.toNormalizedChainCom…SSet.chainComplexMap_PInfty_assoc · cited by 0SSet.chainComplexMap_PInf…CategoryTheory.SimplicialObject.Homotopy.singularChainComplexFunctorObjMap · cited by 0Homotopy.singularChainCom…singularChainComplexFunctor_mapHomotopy_of_simplicialHomotopy · cited by 0singularChainComplexFunct…SSet.Homotopy.singularChainComplexFunctorObjMap · cited by 0Homotopy.singularChainCom…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveSimplexCategory · cited by 2204SimplexCategorySSet · cited by 1283SSetComplexShape.down · cited by 605ComplexShape.downChainComplex · cited by 350ChainComplexCategoryTheory.Limits.HasCoproducts · cited by 119Limits.HasCoproductsSSet.chainComplex · cited by 46SSet.chainComplexSSet.chainComplexFunctor · cited by 3SSet.chainComplexFunctorSSet.chainComplexMapCITED BYCITES

Cites13

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Cited by15

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