  We introduce and study a new class of morphisms which includes morphisms
represented by monomorphisms in the sense of Auslander and Bridger. As an
application, we give not only an extension of Kato's theorem on morphisms
represented by monomorphisms, but also a common generalization of several
results due to Auslander and Bridger that describe relationships between
torsionfreeness and the grades of Ext modules.
