Definition Under_precategories_mor_mor {c c' : C} (h : C⟦c, c'⟧) (af af' : c' / C) (g : (c' / C)⟦af, af'⟧) : (c / C) ⟦Under_precategories_mor_ob h af, Under_precategories_mor_ob h af'⟧. Proof. exists (Under_mor_mor C c' g). exact (Under_precategories_mor_mor_eq h af af' g). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors.