Is there a name for this structure?

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.