This paper deals with the
general problem of determining conditions under which the representability of a given
functor G: A −→Ens implies the representability of a subfunctor F : B−→ Ens of
the restriction of G to a subcategory B of A. With suitable conditions on A and B a
set of necessary and sufficient conditions for the representability of such a
functor F can be obtained. A few examples are given which indicate the
connection between this case of relative or induced representability and universal
algebra.