Theorems · Theorem · category theory

CochainComplex.HomComplex.Cocycle.toSingleMk_neg

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

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle

Cited by

1 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObject