English
There is a canonical family of functors from C to DerivedCategory C, indexed by integers ℤ, called the singleFunctors, which encode the shift action by ℤ on objects of C as complexes concentrated in a single degree.
Русский
Существует каноническаяFamily функторов из C в DerivedCategory C, индексируемая целыми ℤ, называемая одиночныеFunctors, кодирующая действие сдвига ℤ на объекты C через цепочки, сосредоточенные в одном степени.
LaTeX
$$$\text{singleFunctors} : \mathcal{C} \to \mathrm{DerivedCategory}(\mathcal{C})^{\mathbb{Z}}$$$
Lean4
/-- The single functors `C ⥤ DerivedCategory C` for all `n : ℤ` along with
their compatibilities with shifts. -/
noncomputable def singleFunctors : SingleFunctors C (DerivedCategory C) ℤ :=
(HomotopyCategory.singleFunctors C).postcomp Qh
