If "C" and "D" are M-categories (that is, categories enriched over monoidal category M), an M-enriched functor "T": "C" → "D" is a map which assigns to each object of "C" an object of "D" and for each pair of objects "a" and "b" in "C" provides a morphism in M "Tab" : "C"("a", "b") → "D"("T"("a"), "T"("b")) between the hom-objects of "C" and "D" (which are objects in M), satisfying enriched versions of the axioms of a functor, viz preservation of identity and composition.