Monoidal structures on graded categories
Conditions which imply Morita equivalences of functor categories are described. As an application a Dold-Kan type theorem for functors defined on a category associated to associative algebras with one-side units is proved.
We give a classification of ℤ/2ℤ-graded fusion categories whose 0-component is a pointed fusion category. A number of concrete examples are considered.