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

[Tony Morris]

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On 01/20/2012 07:24 AM, Sean Leather 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
> 
> 
> 
> 
> _______________________________________________
> Haskell-Cafe mailing list
> Haskell-Cafe at haskell.org
> http://www.haskell.org/mailman/listinfo/haskell-cafe

It is not clear to me exactly what you are asking, so shot in the dark:
injection or surjection?


- -- 
Tony Morris
http://tmorris.net/

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