On Thu, Jan 19, 2012 at 3:24 PM, Sean Leather <[email protected]> wrote: > I have two types A and B, and I want to express that the composition of two > functions f :: B -> A and g :: A -> B gives me the identity idA = f . g :: A > -> A. I don't need g . f :: B -> B to be the identity on B, so I want a > weaker statement than isomorphism. > > I understand that: > (1) If I look at it from the perspective of f, then g is the right inverse > or section (or split monomorphism). > (2) If I look at from g, then f is the left inverse or retraction (or split > epimorphism). > > But I just want two functions that give me an identity on one of the two > types and I don't care which function's perspective I'm looking at it from. > Is there a word for that? >
I don't think it makes sense to say you want one label for the situation when looking from either end - the relation you're labeling is non-symmetric. > Regards, > Sean > > _______________________________________________ > Haskell-Cafe mailing list > [email protected] > http://www.haskell.org/mailman/listinfo/haskell-cafe > _______________________________________________ Haskell-Cafe mailing list [email protected] http://www.haskell.org/mailman/listinfo/haskell-cafe
