Theorems · Theorem · algebraic topology

SSet.homologyMap_comp_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasCoproducts C]
  [inst_2 : CategoryTheory.Preadditive C] (X Y Z : SSet) (f : X ⟶ Y) (g : Y ⟶ Z) (R : C)
  [inst_3 : CategoryTheory.CategoryWithHomology C] (n : ℕ) {Z_1 : C} (h : Z.homology R n ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (SSet.homologyMap (CategoryTheory.CategoryStruct.comp f g) R n) h =
    CategoryTheory.CategoryStruct.comp (SSet.homologyMap f R n)
      (CategoryTheory.CategoryStruct.comp (SSet.homologyMap g R n) h)

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.Homology.Basic

Cited by

0 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasCoproductsCategoryTheory.PreadditiveCategoryTheory.CategoryWithHomology