  We develop a theory of categories which are simultaneously (1) indexed over a
base category S with finite products, and (2) enriched over an S-indexed
monoidal category V. This includes classical enriched categories, indexed and
fibered categories, and internal categories as special cases. We then describe
the appropriate notion of "limit" for such enriched indexed categories, and
show that they admit "free cocompletions" constructed as usual with a Yoneda
embedding.
