Axis alignment in Xy-pic diagrams

By default, Xy-pic aligns diagrams according to the center of each object. For many types of diagrams, such center alignment is the preferred choice; however, axis alignment is sometimes better. (In fact, simple TEX code like $A \to A^2$ uses axis alignment.) This article studies attempts to instruct Xy-pic to use axis alignment and presents a concise solution to the problem. Enhancements to Xy-pic are proposed.