  The 2-category V-Cat of categories enriched over a braided monoidal category
V is not itself braided in any way that is based upon the braiding of V. The
exception is the case in which V is symmetric, which leads to V-Cat being
symmetric as well. This paper describes how these facts are related to a
categorical analogue of topological delooping. It seems that the analogy of
loop spaces is a good guide for how to define the concept of enrichment over
various types of monoidal objects, including k-fold monoidal categories and
their higher dimensional counterparts. The main result is that for V a k-fold
monoidal category, V-Cat becomes a (k-1)-fold monoidal 2-category in a
canonical way. I indicate how this process may be iterated by enriching over
V-Cat, along the way defining the 3-category of categories enriched over V-Cat.
