  We begin with a brief sketch of what is known and conjectured concerning
braided monoidal 2-categories and their applications to 4d topological quantum
field theories and 2-tangles (surfaces embedded in 4-dimensional space). Then
we give concise definitions of semistrict monoidal 2-categories and braided
monoidal 2-categories, and show how these may be unpacked to give long explicit
definitions similar to, but not quite the same as, those given by Kapranov and
Voevodsky. Finally, we describe how to construct a semistrict braided monoidal
2-category Z(C) as the `center' of a semistrict monoidal category C. This is
analogous to the construction of a braided monoidal category as the center, or
`quantum double', of a monoidal category. As a corollary, our construction
yields a strictification theorem for braided monoidal 2-categories.
