Opposite differential graded functors #
The opposite of a DG functor uses its original chain map on each reversed Hom complex. Thus its action on homogeneous morphisms is unchanged after reversing sources and targets. This is the functorial counterpart of the Koszul-signed opposite DG category.
References #
- B. Keller, Deriving DG categories, Section 1.
theorem
CategoryTheory.EnrichedFunctor.op_dgMap
{R : Type v}
[CommRing R]
{C : Type u₁}
{D : Type u₂}
[TauCeti.DGCategory R C]
[TauCeti.DGCategory R D]
(F : EnrichedFunctor (CochainComplex (ModuleCat R) ℤ) C D)
{X Y : Cᵒᵖ}
(n : ℤ)
(f : TauCeti.DGHom R n (Opposite.unop Y) (Opposite.unop X))
:
The opposite DG functor acts on a homogeneous morphism by the original functor's degreewise map, with its source and target reversed.