fact: Definition preserves_unit {C D : category} (IC : C) (ID : D) (F : functor C D) : UU := D⟦ID, (pr1 F) IC⟧.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos