Definition Initial_functor_precat : Initial [C, D]. Proof. use make_Initial. - exact (constant_functor _ _ ID). - intros F. use tpair. + use make_nat_trans. * intro a; apply InitialArrow. * abstract (intros a b f; apply InitialArrowEq). + abstract (intros α; apply (nat_trans_eq D); intro a; apply InitialArrowUnique). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.Limits.Coproducts.