Mathlib Map

Theorems · Definition · algebraic topology

SSet.fromNormalizedChainComplex

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

The split mono X.normalizedChainComplex R ⟶ X.chainComplex R.

Defined in
Mathlib.AlgebraicTopology.SimplicialSet.Homology.Nondegenerate
Cited by
12 results in Mathlib
Foundations
Depth 100 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.normalizedChainComplexMap · cited by 5SSet.normalizedChainCompl…SSet.fromNormalizedChainComplex_toNormalizedChainComplex · cited by 2SSet.fromNormalizedChainC…SSet.toNormalizedChainComplex_fromNormalizedChainComplex · cited by 2SSet.toNormalizedChainCom…SSet.ιNormalizedChainComplex_fromNormalizedChainComplex_f · cited by 2SSet.ιNormalizedChainComp…SSet.toNormalizedChainComplex_f_fromNormalizedChainComplex_f · cited by 2SSet.toNormalizedChainCom…SSet.fromNormalizedChainComplex_f_toNormalizedChainComplex_f · cited by 1SSet.fromNormalizedChainC…SSet.toNormalizedChainComplex_fromNormalizedChainComplex_assoc · cited by 1SSet.toNormalizedChainCom…SSet.toNormalizedChainComplex_f_fromNormalizedChainComplex_f_assoc · cited by 0SSet.toNormalizedChainCom…SSet.fromNormalizedChainComplex_f_toNormalizedChainComplex_f_assoc · cited by 0SSet.fromNormalizedChainC…SSet.fromNormalizedChainComplex_toNormalizedChainComplex_assoc · cited by 0SSet.fromNormalizedChainC…SSet.homotopyEquivNormalizedChainComplex_inv · cited by 0SSet.homotopyEquivNormali…SSet.ιNormalizedChainComplex_eq_zero · cited by 0SSet.ιNormalizedChainComp…SSet.ιNormalizedChainComplex_fromNormalizedChainComplex_f_assoc · cited by 0SSet.ιNormalizedChainComp…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveSSet · cited by 1283SSetComplexShape.down · cited by 605ComplexShape.downChainComplex · cited by 350ChainComplexCategoryTheory.Limits.HasCoproducts · cited by 119Limits.HasCoproductsSSet.chainComplex · cited by 46SSet.chainComplexSSet.normalizedChainComplex · cited by 29SSet.normalizedChainCompl…CategoryTheory.Limits.sigmaConst · cited by 18Limits.sigmaConstCategoryTheory.SimplicialObject.Splitting.fromNondegComplex · cited by 7Splitting.fromNondegCompl…SSet.splitting · cited by 5SSet.splittingCategoryTheory.SimplicialObject.Splitting.map · cited by 5Splitting.mapSSet.fromNormalizedChainCompl…CITED BYCITES

Cites14

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Cited by13

Results whose statement or proof uses this declaration.