Lemma Comonad_eq_raw_data (C : category) (T T' : Comonad C) : Comonad_to_raw_data T = Comonad_to_raw_data T' -> T = T'. Proof. intro e. apply (invmaponpathsweq (_,, (isweq_iso _ _ (@Comonad_to_Comonad'_to_Comonad C) (@Comonad'_to_Comonad_to_Comonad' C)))). now apply (Comonad'_eq_raw_data C). Qed.
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.