Definition constant_nat_trans (C₁ : category) {C₂ : category} {x y : C₂} (f : x --> y) : nat_trans (constant_functor C₁ C₂ x) (constant_functor C₁ C₂ y). Proof. use make_nat_trans. - exact (λ _, f). - abstract (intros ? ? ? ; cbn ; rewrite id_left, id_right ; apply idpath). Defined.
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.