[Haskell-cafe] Not an isomorphism, but what to call it?
Dan Doel
dan.doel at gmail.com
Thu Jan 19 23:21:28 CET 2012
A is a retract of B.
http://nlab.mathforge.org/nlab/show/retract
g is the section, f is the rectraction. You seem to have it already.
The definition needn't be biased toward one of the functions.
On Thu, Jan 19, 2012 at 4:24 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?
>
> Regards,
> Sean
>
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