Scalars on the unit of the doubling #
The unit of the doubling is the unit in even degree and the zero object in odd degree, so its endomorphisms are those of the unit downstairs: the scalar-unit hypothesis passes to the doubling.
theorem
RS.hasScalarUnit_doubled
{A : Type u}
[CategoryTheory.Category.{v, u} A]
[CategoryTheory.MonoidalCategory A]
[CategoryTheory.Preadditive A]
[CategoryTheory.Linear ℂ A]
[CategoryTheory.MonoidalPreadditive A]
[CategoryTheory.Limits.HasBinaryBiproducts A]
[CategoryTheory.Limits.HasZeroObject A]
(hu : HasScalarUnit A)
:
HasScalarUnit (Doubled A)
The scalar-unit hypothesis passes to the doubling.