Title: Semisimple and separable algebras in multi-fusion categories,
Abstract: We give a classification of semisimple and separable algebras in a
multi-fusion category over an arbitrary field in analogy to Wedderben-Artin
theorem in classical algebras. It turns out that, if the multi-fusion category
admits a semisimple Drinfeld center, the only obstruction to the separability
of a semisimple algebra arises from inseparable field extensions as in
classical algebras. Among others, we show that a division algebra is separable
if and only if it has a nonvanishing dimension.