  This paper is a contribution to the construction of non-semisimple modular
categories. We establish when M\"uger centralizers inside non-semisimple
modular categories are also modular. As a consequence, we obtain conditions
under which relative monoidal centers give (non-semisimple) modular categories,
and we also show that examples include representation categories of small
quantum groups. We further derive conditions under which representations of
more general quantum groups, braided Drinfeld doubles of Nichols algebras of
diagonal type, give (non-semisimple) modular categories.
