Definition limOfArrows {g : graph} {d1 d2 : diagram g C^op} (CC1 : LimCone d1) (CC2 : LimCone d2) (f : ∏ (u : vertex g), C⟦dob d1 u,dob d2 u⟧) (fNat : ∏ u v (e : edge u v), f v · (dmor d2 e : C⟦dob d2 v, dob d2 u⟧) = (dmor d1 e : C⟦dob d1 v, dob d1 u⟧)· f u) : C⟦lim CC1 , lim CC2⟧. Proof. use (colimOfArrows CC2 CC1). - apply f. - apply fNat. 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.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Import UniMath.CategoryTheory.opp_precat.