Re: [Haskell-cafe] Not an isomorphism, but what to call it?
On Thu, Jan 19, 2012 at 23:21, Dan Doel wrote: 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. Great! That's what I was looking for. Thanks! ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Not an isomorphism, but what to call it?
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@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Not an isomorphism, but what to call it?
On Thu, Jan 19, 2012 at 3:24 PM, Sean Leather leat...@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 ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Not an isomorphism, but what to call it?
-BEGIN PGP SIGNED MESSAGE- Hash: SHA1 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@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/ -BEGIN PGP SIGNATURE- Version: GnuPG v1.4.11 (GNU/Linux) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org/ iQEcBAEBAgAGBQJPGJNXAAoJEPxHMY3rBz0PHt0IAKP1lVcfDXZm00h4W1WQPDBT h6LB9nLlp0cgAh5CH06FsdQFqdtDVJNMkV7/9q3H/wTFOoscZHCTigr1G+vE/kA8 lh1/Gb3caQByt6rWkgD79998FL5ZCBdHN2HYh1o/RPBwA/BYxA041P92pE0EFTKB 1oylh5ldUfv8rEzvHhQVw0USrJ11uiZfn/T3+UrO2s2xLQZS1oTWNZhsKMccjB95 tYaqEw+20Q+8yBanVnDJFOqD3yPXIRBHkTSJTOFO+Y++oen4gXUzSJJ2lkpXLECE ojMNHD/9Yh43gCm1Jq3Wuz5B6mr+v+RTRuLkxiVMsK7wxW+lfmOgeMyxHyr8pxU= =aPtB -END PGP SIGNATURE- ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Not an isomorphism, but what to call it?
Am 19.01.2012 um 22:24 schrieb Sean Leather: 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? If (g . f) is a closure operator for some ordering on B, then f,g is a Galois insertion, a special case of Galois connection. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Not an isomorphism, but what to call it?
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 leat...@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 ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
