Finite semisimple module 2-categories

Let \(\mathfrak {C}\) $\mathfrak{C}$ be a multifusion 2-category. We show that every finite semisimple \(\mathfrak {C}\) $\mathfrak{C}$ -module 2-category is canonically enriched over \(\mathfrak {C}\) $\mathfrak{C}$ . Using this enrichment, we prove that every finite semisimple \(\mathfrak {C}\) $\mathfrak{C}$ -module 2-category is equivalent to the 2-category of modules over a rigid algebra in \(\mathfrak {C}\) $\mathfrak{C}$ .