Definition functors_eq_data_to_unitary_functors_eq (u : is_univalent_dagger dagD) : functors_eq_data -> unitary_functors_eq. Proof. intro p. exists (λ c, idtodaggeriso dagD _ _ (pr1 p c)). intros x y f. refine (pr2 p x y f @ _). do 2 apply maponpaths_2. etrans. { apply (idtodaggeriso_is_dagger_of_idtodaggeriso dagD). } do 3 apply maponpaths. apply pathsinv0inv0. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. 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.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DaggerCategories.Categories. Require Import UniMath.CategoryTheory.DaggerCategories.Unitary. Require Import UniMath.CategoryTheory.DaggerCategories.Univalence. Require Import UniMath.CategoryTheory.DaggerCategories.Functors. Require Import UniMath.CategoryTheory.DaggerCategories.Transformations.