Theorems · Theorem · category theory

CochainComplex.HomComplex.Cochain.fromSingleMk_precomp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  [inst_2 : CategoryTheory.Limits.HasZeroObject C] {X : C} {K : CochainComplex C ℤ} {X' : C} (g : X' ⟶ X) {p q : ℤ}
  (f : X ⟶ K.X q) {n : ℤ} (h : p + n = q),
  CochainComplex.HomComplex.Cochain.fromSingleMk (CategoryTheory.CategoryStruct.comp g f) h =
    (CochainComplex.HomComplex.Cochain.ofHom ((CochainComplex.singleFunctor C p).map g)).comp
      (CochainComplex.HomComplex.Cochain.fromSingleMk f h) ⋯

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle

Cited by

1 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObject