Section MulFun.
Variables (R : ringType) (U : zmodType).
Variables (a : R) (f : {additive U -> R}).
Fact mull_fun_is_additive : additive (a \*o f).
Canonical in_alg_additive := Additive in_alg_is_rmorphism.
Canonical in_alg_rmorphism := RMorphism in_alg_is_rmorphism.

Lemma in_algE a : in_alg_loc A a = a%:A. Proof. by []. Qed.