Section Class_Def.
Variables aT rT : FalgType K.
Definition ahom_in (U : {vspace aT}) (f : 'Hom(aT, rT)) :=
all2rel (fun x y : aT => f (x * y) == f x * f y) (vbasis U) && (f 1 == 1).

Lemma ahom_inP {f : 'Hom(aT, rT)} {U : {vspace aT}} :
reflect ({in U &, {morph f : x y / x * y >-> x * y}} * (f 1 = 1))
(ahom_in U f).