Multi-fusion categories are a generalization of fusion categories with a non-simple unit. The direct sum of two multi-fusion categories is again a multi-fusion category. By irreducible I mean that a multi-fusion category cannot be written as a non-trivial direct sum. Are all such irreducible multi-fusion categories fusion categories?
Bonus question: Are there multi-fusion categories that are not Morita equivalent to a direct sum of fusion categories?
[I'm mainly interested in the unitary case.]