Definition proj_comm {C I:category} {D: I⟶C} (lim:Limit D) {i j:I} (f:i-->j) : # D f ∘ proj_ lim i = proj_ lim j. Proof. intros. exact (pr2 (universalElement lim) _ _ f). Defined.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import Require Import Require Import UniMath.MoreFoundations.Tactics.