Stability of semisimple categories?
If a category is not semi simple, are its higher categories semisimple? I.e, does the property of semisimiplicity stabilize?
Linear representations
The category of (finite) linear representations of a finite group (see details in Representation of a group) is semisimple; this is the content of Maschke’s Theorem.
A natural starting point is to ask if the corresponding 2-category is semisimple. Let’s describe this now. Calling the category of representations as specified above $C$, we wish to show that maps between representations, i.e. the morphisms of $C$, are semisimple. Let us first regard the simple objects.