Definition free_abgr_extend {X : hSet} {Y : abgr} (f : X → Y) : monoidfun (free_abgr X) Y. Proof. apply (presented_gr_extend f). unfold iscomprelfun. apply free_abgr_hrel_univ. - intros. apply (isasetmonoid Y). - intros x y. rewrite !monoidfunmul. apply (commax Y). 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.