Definition monoid_mor_eq {X Y : monoid_ob} {f g : monoid_mor X Y} : (f : X --> Y) = g ≃ f = g. Proof. apply invweq. apply subtypeInjectivity. intro. apply isaprop_is_monoid_mor. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored.