Theorems · Theorem · category theory

CochainComplex.HomComplex.Cocycle.fromSingleMk_add

∀ {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} {p q : ℤ} (f g : X ⟶ K.X q) {n : ℤ}
  (h : p + n = q) (q' : ℤ) (hq' : q + 1 = q') (hf : CategoryTheory.CategoryStruct.comp f (K.d q q') = 0)
  (hg : CategoryTheory.CategoryStruct.comp g (K.d q q') = 0),
  CochainComplex.HomComplex.Cocycle.fromSingleMk (f + g) h q' hq' ⋯ =
    CochainComplex.HomComplex.Cocycle.fromSingleMk f h q' hq' hf +
      CochainComplex.HomComplex.Cocycle.fromSingleMk g h q' hq' hg

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle

Cited by

1 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObject