On the relationship between hierarchy and type morphisms

Here, we establish a relationship between hierarchy and type morphisms. Both concepts have been used to relate the types in one structure to types in a second “larger” structure. In general, the two concepts may differ, in the sense that a hierarchy morphism need not be a type morphism. We provide a necessary and sufficient condition under which the two concepts coincide. We go on to provide situations under which this condition must be satisfied.