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@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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