  Restriction categories were introduced to provide an axiomatic setting for
the study of partially defined mappings; they are categories equipped with an
operation called restriction which assigns to every morphism an endomorphism of
its domain, to be thought of as the partial identity that is defined to just
the same degree as the original map. In this paper, we show that restriction
categories can be identified with \emph{enriched categories} in the sense of
Kelly for a suitable enrichment base. By varying that base appropriately, we
are also able to capture the notions of join and range restriction category in
terms of enriched category theory.
