  In this paper, we study the relation between an anomaly-free $n+$1D
topological order, which are often called $n+$1D topological order in physics
literature, and its $n$D gapped boundary phases. We argue that the $n+$1D bulk
anomaly-free topological order for a given $n$D gapped boundary phase is
unique. This uniqueness defines the notion of the "bulk" for a given gapped
boundary phase. In this paper, we show that the $n+$1D "bulk" phase is given by
the "center" of the $n$D boundary phase. In other words, the geometric notion
of the "bulk" corresponds precisely to the algebraic notion of the "center". We
achieve this by first introducing the notion of a morphism between two
(potentially anomalous) topological orders of the same dimension, then proving
that the notion of the "bulk" satisfies the same universal property as that of
the "center" of an algebra in mathematics, i.e. "bulk = center". The entire
argument does not require us to know the precise mathematical description of a
(potentially anomalous) topological order. This result leads to concrete
physical predictions.
