Theorems · Theorem · algebraic topology

AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_naturality_assoc

∀ {A : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} A] [inst_1 : CategoryTheory.Abelian A]
  {X Y : CategoryTheory.SimplicialObject A} (f : X ⟶ Y) {Z : ChainComplex A ℕ}
  (h : AlgebraicTopology.NormalizedMooreComplex.obj Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp (AlgebraicTopology.AlternatingFaceMapComplex.map f)
      (CategoryTheory.CategoryStruct.comp (AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex Y) h) =
    CategoryTheory.CategoryStruct.comp (AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex X)
      (CategoryTheory.CategoryStruct.comp (AlgebraicTopology.NormalizedMooreComplex.map f) h)

Defined in

Mathlib.AlgebraicTopology.DoldKan.Normalized

Cited by

0 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian