Lemma LimFunctorCone : LimCone D. Proof. use make_LimCone. - exact LimFunctor. - use make_cone. + now apply lim_nat_trans_in_data. + abstract (now intros u v e; apply (nat_trans_eq hsC); intro a; apply (limOutCommutes (HCg a))). - now intros F cc; simpl; apply (LimFunctor_unique _ cc). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Propositions. 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.