Lemma limArrowUnique {J C : precategory} {F : functor J C} (CC : LimCone F) (c : C) (cc : cone F c) (k : C⟦c, lim CC⟧) (Hk : ∏ u, k · limOut CC u = coneOut cc u) : k = limArrow CC c cc. Proof. now apply path_to_ctr, Hk. Qed.
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.