Theorems · Theorem · category theory

CochainComplex.HomComplex.Cochain.leftShift_v

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

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift

Cited by

19 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive