Lemma isaset_disp_nat_trans {C' C : category} {D' : disp_cat C'} {D : disp_cat C} {x y : functor C' C} (f : nat_trans x y) (xx : disp_functor x D' D) (yy : disp_functor y D' D) : isaset (disp_nat_trans f xx yy). Proof. intros. simpl in *. apply (isofhleveltotal2 2). * do 2 (apply impred; intro). apply homsets_disp. * intro d. do 6 (apply impred; intro). apply hlevelntosn. apply homsets_disp. Qed.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Isos.