Definition comonads_category_disp : disp_cat [C,C]. Proof. use disp_cat_from_SIP_data. - intro F. exact (∑ T : disp_Comonad_data F, disp_Comonad_laws T). - intros F F' [T Tlaws] [T' T'laws] α. exact (disp_Comonad_Mor_laws T T' α). - intros F F' [T Tlaws] [T' T'laws] α. apply isaprop_disp_Comonad_Mor_laws. - intros F [T Tlaws]. apply (comonads_category_id_subproof _ Tlaws). - intros F F' F'' [T Tlaws] [T' T'laws] [T'' T''laws] α α'. apply (comonads_category_comp_subproof _ Tlaws _ T'laws _ T''laws). 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.Notations. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.SIP. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.Core.Univalence.