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It dates back to at least the original paper on category theory by Mac Lane and Eilenberg (General theory of natural equivalences), on page 14: "For abelian groups there is a similar functor "Hom." Specifically, let G be a locally compact regular topological group, H a topological abelian group. We construct the set Hom (G, H) of all (continuous) homomorphisms phi of G into H. The sum of two such homomorphisms phi1 and phi2 is defined by setting (phi1+phi2)g=phi1g+phi2g, for each g in G; this sum is itself a homomorphism because H is abelian." -Ian ----- Original Message ----- From: "Derek Dreyer" <[email protected]> To: "Types list" <[email protected]> Sent: Wednesday, November 5, 2014 12:51:30 PM GMT -05:00 US/Canada Eastern Subject: [TYPES] origin of the term "hom-set"? [ 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? Thanks, Derek
