Definition free_abmonoid_extend {X : hSet} {Y : abmonoid} (f : X → Y) : monoidfun (free_abmonoid X) Y. Proof. apply (presented_monoid_extend f). unfold iscomprelfun. apply free_abmonoid_hrel_univ. - intros. apply (isasetmonoid Y). - intros x y. rewrite !monoidfunmul. apply commax. Defined.
Require Import UniMath.MoreFoundations.Subtypes. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.IteratedBinaryOperations. Require Import UniMath.Combinatorics.Lists.