Lemma nat_trans_eq {C C' : precategory_data} (hs: has_homsets C') (F F' : functor_data C C')(a a' : nat_trans F F'): (∏ x, a x = a' x) -> a = a'. Proof. intro H. assert (H' : pr1 a = pr1 a'). { now apply funextsec. } apply (total2_paths_f H'), proofirrelevance, isaprop_is_nat_trans, hs. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.TransportMorphisms. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Univalence.