  In this work, inspired by some physical intuitions, we define a series of
symmetry enriched categories to describe symmetry enriched topological (SET)
orders, and define a new tensor product, called the relative tensor product,
which describes the stacking of 2+1D SET orders. Then we choose and modify the
domain and codomain categories, and manage to make the Drinfeld center a fully
faithful symmetric monoidal functor. It turns out that this functor, named the
symmetry enriched center functor, provides a precise and rather complete
mathematical formulation of the boundary-bulk relation of symmetry enriched
topological (SET) orders. We also provide another description of the relative
tensor product via a condensable algebra.
