[Haskell-cafe] Not an isomorphism, but what to call it?

Antoine Latter aslatter at gmail.com
Thu Jan 19 22:46:13 CET 2012

On Thu, Jan 19, 2012 at 3:24 PM, Sean Leather <leather at cs.uu.nl> 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
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