  In this paper, we study the relation between topological orders and their
gapped boundaries. We propose that the bulk for a given gapped boundary theory
is unique. It is actually a consequence of a microscopic definition of a local
topological order, which is a (potentially anomalous) topological order defined
on an open disk. Using this uniqueness, we show that the notion of "bulk" is
equivalent to the notion of center in mathematics. We achieve this by first
introducing the notion of a morphism between two local topological orders of
the same dimension, then proving that the bulk satisfying the same universal
property as that of the center in mathematics. We propose a classification
(formulated as a macroscopic definition) of $n+$1D local topological orders by
unitary multi-fusion $n$-categories, and explain that the notion of a morphism
between two local topological orders is compatible with that of a unitary
monoidal $n$-functor in a few low dimensional cases. We also explain in some
low dimensional cases that this classification is compatible with the result of
"bulk = center". In the end, we explain that above boundary-bulk relation is
only the first layer of a hierarchical structure which can be summarized by the
functoriality of the bulk (or center). This functoriality also provides the
physical meanings of some well-known mathematical results on fusion
1-categories. This work can also be viewed as the first step towards a
systematic study of the category of local topological orders, and the
boundary-bulk relation actually provides a useful tool for this study.
