Theorems · Theorem · algebraic topology

SSet.toNormalizedChainComplex_normalizedChainComplexMap_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasCoproducts C]
  [inst_2 : CategoryTheory.Preadditive C] {X Y : SSet} (f : X ⟶ Y) (R : C) {Z : ChainComplex C ℕ}
  (h : Y.normalizedChainComplex R ⟶ Z),
  CategoryTheory.CategoryStruct.comp (X.toNormalizedChainComplex R)
      (CategoryTheory.CategoryStruct.comp (SSet.normalizedChainComplexMap f R) h) =
    CategoryTheory.CategoryStruct.comp (SSet.chainComplexMap f R)
      (CategoryTheory.CategoryStruct.comp (Y.toNormalizedChainComplex R) h)

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.Homology.Nondegenerate

Cited by

0 results in Mathlib

Foundations

Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasCoproductsCategoryTheory.Preadditive