fact: Definition identityfunctor_preserves_unit {C : category} (IC : C) : preserves_unit IC IC (functor_identity C) := identity IC.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos