  In this paper we study the relative tensor product of module categories over
braided fusion categories using, in part, the notion of the relative center of
a module category. In particular we investigate the canonical tensor category
structure and braiding inherited by the relative tensor product when module
categories are themselves tensor/braided. As a basic example we show that the
category of representations of the fibre product of finite groups may be
expressed in terms of the relative product and show how to multiply braided
fusion categories arising from pre-metric groups. Also, we consider relative
centers of braided fusion categories and look at the relative tensor product
over Muger centers. We finish with an in-depth example hinting at a
categorification of conjugacy classes for finite groups.
