instAdditiveShiftFunctorInt — Mathlib

English

The functor Q on CochainComplex with integer indexing is additive; it preserves finite biproducts in the cochain setting.

Русский

Функтор Q на коCHAIN-цепочках с индексами по целым аддитивен; сохраняет конечные биаддитивности.

LaTeX

$$$\mathrm{Q.Additive} : \mathrm{CochainComplex}(\mathcal{C}; \mathbb{Z}) \to \mathrm{DerivedCategory}(\mathcal{C})$$$

Lean4

instance (n : ℤ) : (shiftFunctor (DerivedCategory C) n).Additive :=
  by
  rw [Localization.functor_additive_iff Qh (HomotopyCategory.subcategoryAcyclic C).trW]
  exact Functor.additive_of_iso (Qh.commShiftIso n)

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