  Lyubashenko has described enriched 2-categories as categories enriched over
V-Cat, the 2-category of categories enriched over a symmetric monoidal V. I
have generalized this to the k-fold monoidal V. The symmetric case can easily
be recovered. The introduction of this paper proposes a recursive definition of
V-n-categories and their morphisms. Then I consider the special case of
V-2-categories and give the details of the proof that with their morphisms
these form the structure of a 3-category.
