Definition equality_to_functors_eq_data : pr1 F = pr1 G -> functors_eq_data. Proof. intro p. exists (λ c, eqtohomot (base_paths _ _ p) c). abstract ( intros x y f ; refine (! eqtohomot (eqtohomot (eqtohomot (fiber_paths p) x) y) f @ _) ; etrans ; [ apply transport_of_dagger_functor_map_is_pointwise | apply double_transport_idtodaggeriso] ). 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.