Lemma setquot_map_epi {X : Type} {R : eqrel X} {Y : hSet} {h h' : setquot R → Y} : h ∘ setquotpr R ~ h' ∘ setquotpr R -> h ~ h'. Proof. use (surjectionisepitosets _ _ _ (issurjsetquotpr R) (setproperty Y)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.Free_Monoids_and_Groups.