  Given a precovering (also called contravariantly finite) class F there are
three natural approaches to a homological dimension with respect to F: One
based on Ext functors relative to F, one based on F-resolutions, and one based
on Schanuel classes relative to F. In general these approaches do not give the
same result. In this paper we study relations between the three approaches
above, and we give necessary and sufficient conditions for them to agree.
