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Theorems · Definition · algebraic topology

SSet.homology

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [CategoryTheory.Limits.HasCoproducts C] →
      [inst_2 : CategoryTheory.Preadditive C] → SSet → C → [CategoryTheory.CategoryWithHomology C] → ℕ → C

The simplicial homology with coefficients in R : C in degree n of a simplicial set X.

Defined in
Mathlib.AlgebraicTopology.SimplicialSet.Homology.Basic
Cited by
13 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasCoproductsCategoryTheory.PreadditiveCategoryTheory.CategoryWithHomology

Around this declaration

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

SSet.homologyMap · cited by 9SSet.homologyMapSSet.homology₀Iso · cited by 3SSet.homology₀IsoSSet.homologyFunctor · cited by 2SSet.homologyFunctorSSet.homology₀ε · cited by 2SSet.homology₀εCategoryTheory.SimplicialObject.Homotopy.congr_sSetHomologyMap · cited by 2Homotopy.congr_sSetHomolo…SSet.homologyMap_comp · cited by 1SSet.homologyMap_compSSet.liftCycles_ιChainComplex_homologyπ_homology₀Iso_hom · cited by 1SSet.liftCycles_ιChainCom…SSet.liftCycles_ιChainComplex_homologyπ_homology₀Iso_hom_assoc · cited by 1SSet.liftCycles_ιChainCom…SSet.Homotopy.congr_homologyMap · cited by 1Homotopy.congr_homologyMapCategoryTheory.SimplicialObject.Homotopy.singularChainComplexFunctor_map_homology_eq_of_simplicialHomotopy · cited by 0Homotopy.singularChainCom…SSet.homologyFunctor_map · cited by 0SSet.homologyFunctor_mapSSet.homologyFunctor_obj · cited by 0SSet.homologyFunctor_objSSet.homologyMap_comp_assoc · cited by 0SSet.homologyMap_comp_ass…SSet.homologyMap_id · cited by 0SSet.homologyMap_idSSet.isZero_homology_of_hasDimensionLT · cited by 0SSet.isZero_homology_of_h…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveSSet · cited by 1283SSetHomologicalComplex.homology · cited by 209HomologicalComplex.homolo…CategoryTheory.Limits.HasCoproducts · cited by 119Limits.HasCoproductsCategoryTheory.CategoryWithHomology · cited by 116CategoryTheory.CategoryWi…SSet.chainComplex · cited by 46SSet.chainComplexSSet.homologyCITED BYCITES

Cites7

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Cited by17

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