[ The Types Forum, http://lists.seas.upenn.edu/mailman/listinfo/types-list ]
Derek Dreyer writes: > [ The Types Forum, http://lists.seas.upenn.edu/mailman/listinfo/types-list ] > > Hi. Does anyone know the origin of the term "hom-set"? It came up > yesterday in class, and after a little googling, I have not turned up > the answer. I always assumed it stood for "homomorphism set" (?) but > even that much I have not been able to verify, and it doesn't explain > why we are talking about "homomorphisms" as opposed to "morphisms" (or > "sets" rather than "collections", since the hom-set is not always a > set). I presume there is some historical reason for this? Originally, "morphism" was a shortened form of "homomorphism". However, some mathematicians these days restrict "homomorphism" to mean a structure-preserving map (as in algebra) whereas morphisms don't have any such requirement. With that terminology, the two are distinct concepts. As for why it should be called a "hom-set", recall that Mac Lane works in a set theory with universes. So, what we call a collection or class is a "set" for him and what we call a set is a "small set". Cheers, Uday
