Is there a name for this structure?

Tom Pledger
Wed, 27 Mar 2002 16:22:29 +1200

Joe English writes:
 | Suppose you have two morphisms f : A -> B and g : B -> A
 | such that neither (f . g) nor (g . f) is the identity,
 | but satisfying (f . g . f) = f.   Is there a conventional name
 | for this?

Is it equivalent to saying that (f . g) is the identity on the range
of f?  That's shorter, though still not a snappy single word term.