[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?

Thanks,
Derek