Theorems · Theorem · category theory

CochainComplex.HomComplex.Cochain.leftUnshift_v

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  {K L : CochainComplex C ℤ} {n' a : ℤ}
  (γ : CochainComplex.HomComplex.Cochain ((CategoryTheory.shiftFunctor (CochainComplex C ℤ) a).obj K) L n') (n : ℤ)
  (hn : n + a = n') (p q : ℤ) (hpq : p + n = q) (p' : ℤ) (hp' : p' + n' = q),
  (γ.leftUnshift n hn).v p q hpq =
    (a * n' + a * (a - 1) / 2).negOnePow •
      CategoryTheory.CategoryStruct.comp (K.shiftFunctorObjXIso a p' p ⋯).inv (γ.v p' q ⋯)

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift

Cited by

2 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive