[TYPES] origin of the term "hom-set"?

J. Ian Johnson ianj at ccs.neu.edu
Wed Nov 5 13:27:00 EST 2014

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."

----- Original Message -----
From: "Derek Dreyer" <dreyer at mpi-sws.org>
To: "Types list" <types-list at lists.seas.upenn.edu>
Sent: Wednesday, November 5, 2014 12:51:30 PM GMT -05:00 US/Canada Eastern
Subject: [TYPES] origin of the term "hom-set"?

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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?


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