We define the class of rigid Frobenius algebras in a (non-semisimple) modular category and prove that their categories local modules are, again, modular. This generalizes previous work Kirillov Ostrik (Adv Math 171(2):183–227, 2002) semisimple setup. Examples non-semisimple via modules, as well connections to authors’ prior on relative monoidal centers, are provided. In particular, we classify ...