Definition isLimCone {J C : precategory} (F : functor J C) (l : C) (cc0 : cone F l) : UU := ∏ (c : C) (cc : cone F c), iscontr (∑ x : C⟦c,l⟧, ∏ v, x · coneOut cc0 v = coneOut cc v).
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.