  We introduce the theory of enrichment over an internal monoidal category as a
common generalization of both the standard theories of enriched and internal
categories. The aim of the paper is to justify and contextualize the new notion
by comparing it to other known generalizations of enrichment: namely, those for
indexed categories and for generalized multicategories. It turns out that both
of these notions are closely related to internal enrichment and, as a
corollary, to each other.
