leftDerivedToHomotopyCategory — Mathlib

English

The inverse part of the isomorphism between left-derived objects is natural with respect to maps on objects, compatibly with the resolution maps.

Русский

Обратная часть изоморфизма между левыми производными естественна по отображениям объектов, совместима с маппингами разрешений.

LaTeX

$$$ (P.isoLeftDerivedToHomotopyCategoryObj F).\inv \circ F.map f = \cdots$$$

Lean4

/-- The natural transformation
`F.leftDerivedToHomotopyCategory ⟶ G.leftDerivedToHomotopyCategory` induced by
a natural transformation `F ⟶ G` between additive functors. -/
noncomputable def leftDerivedToHomotopyCategory {F G : C ⥤ D} [F.Additive] [G.Additive] (α : F ⟶ G) :
    F.leftDerivedToHomotopyCategory ⟶ G.leftDerivedToHomotopyCategory :=
  Functor.whiskerLeft _ (NatTrans.mapHomotopyCategory α (ComplexShape.down ℕ))

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