Definition functors_eq_data_from_unitary_functors_eq (u : is_univalent_dagger dagD) : unitary_functors_eq -> functors_eq_data. Proof. intros p. use tpair. - intro c ; apply u ; exact (pr1 p c). - intros x y f. refine (pr2 p x y f @ _). apply maponpaths_compose. + apply maponpaths_2. refine (_ @ ! idtodaggeriso_is_dagger_of_idtodaggeriso dagD _). do 2 apply maponpaths. etrans. * apply pathsinv0, (idtodaggeriso_daggerisotoid u). * apply maponpaths, pathsinv0, pathsinv0inv0. + apply pathsinv0, idtodaggermor_daggerisotoid. 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.