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In this work, inspired by some physical intuitions, we define a series ofsymmetry 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 thedomain and codomain categories, and manage to make the Drinfeld center a fullyfaithful symmetric monoidal functor. It turns out that this functor, named thesymmetry enriched center functor, provides a precise and rather completemathematical formulation of the boundary-bulk relation of symmetry enrichedtopological (SET) orders. We also provide another description of the relativetensor product via a condensable algebra.

The Symmetry Enriched Center Functor is Fully Faithful