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A fusion category is called simple if its fusion subcategories are just $Vec$ and itself. Let us call a fusion category strongly simple if every fusion category Morita equivalent to it (i.e. same ...

This sequel of Is there a strongly noncommutative fusion category? is motivated to know whether every fusion category is "equivalent" (in some sense) to one with a commutative Grothendieck ...

Kaplansky's sixth conjecture [Ka75] states that the dimension of a semisimple finite dimensional Hopf algebra over $\mathbb{C}$ is divisible by the dimension of its irreducible complex representations....