# Is there a name for this structure?

**Joe English
**
jenglish@flightlab.com

*Tue, 26 Mar 2002 20:05:40 -0800*

Not really a Haskell question, but someone here might know the answer...
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? Alternately, same question, but f and g are functors
and A and B categories.
In some cases (g . f . g) is also equal to g; is there a name
for this as well?
I find myself running into pairs of functions with this property
over and over again, and am looking for a short way to describe
the property...
Thanks,
--Joe English
jenglish@flightlab.com