Lemma dagger_transformation_equality {F G : functor C D} {dagF : is_dagger_functor dagC dagD F} {dagG : is_dagger_functor dagC dagD G} (α β : dagger_functor_cat⟦make_dagger_functor dagF , make_dagger_functor dagG⟧) : (∏ x : C, pr11 α x = pr11 β x) -> α = β. Proof. intro p. use subtypePath. { intro ; apply isapropunit. } apply (nat_trans_eq D). exact p. Qed.
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.