proposition: Lemma monoid_equiv_z_iso_is_equiv (X Y : ob monoid_category) : isweq (monoid_equiv_z_iso X Y).
proof: Proof. use isweq_iso. - exact (monoid_z_iso_equiv X Y). - intros y. use monoidiso_paths. use subtypePath. + intros x0. use isapropisweq. + use idpath. - intros x. use z_iso_eq. use monoidfun_paths. use idpath. 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