Monoidal structure on C ⥤ D
when D
is monoidal. #
When C
is any category, and D
is a monoidal category,
there is a natural "pointwise" monoidal structure on C ⥤ D
.
The initial intended application is tensor product of presheaves.
(An auxiliary definition for functorCategoryMonoidal
.)
Tensor product of functors C ⥤ D
, when D
is monoidal.
Instances For
(An auxiliary definition for functorCategoryMonoidal
.)
Tensor product of natural transformations into D
, when D
is monoidal.
Instances For
(An auxiliary definition for functorCategoryMonoidal
.)
Instances For
(An auxiliary definition for functorCategoryMonoidal
.)
Instances For
When C
is any category, and D
is a monoidal category,
the functor category C ⥤ D
has a natural pointwise monoidal structure,
where (F ⊗ G).obj X = F.obj X ⊗ G.obj X
.
When C
is any category, and D
is a braided monoidal category,
the natural pointwise monoidal structure on the functor category C ⥤ D
is also braided.
When C
is any category, and D
is a symmetric monoidal category,
the natural pointwise monoidal structure on the functor category C ⥤ D
is also symmetric.