Definition nat_to_monoid_fun {X : monoid} (x : X) : natset -> X. Proof. intros n. induction n as [ | n IHn]. - exact (unel X). - exact (@op X x IHn). Defined.
Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups.