Lemma limArrowEta {J C : precategory} {F : functor J C} (CC : LimCone F) (c : C) (f : C⟦c, lim CC⟧) : f = limArrow CC c (tpair _ (λ u, f · limOut CC u) (Cone_precompose (limCone CC) c f)). Proof. now apply limArrowUnique. 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.