proposition: Lemma monoid_forgetful_functor_is_faithful : faithful monoid_forgetful_functor.
proof: Proof. unfold faithful. intros ? ?. apply isinclpr1. apply isapropismonoidfun. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.UnivalenceAxiom UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids UniMath.Algebra.Free_Monoids_and_Groups UniMath.Combinatorics.Lists UniMath.Algebra.IteratedBinaryOperations UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Adjunctions.Core