Lemma dagger_functor_equality {C D : category} {dagC : dagger C} {dagD : dagger D} (F G : dagger_functor dagC dagD) : pr11 F = pr11 G -> F = G. Proof. intro p. use subtypePath. { intro ; apply isaprop_is_dagger_functor. } use (functor_eq _ _ (homset_property D)). exact p. 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.DaggerCategories.Categories.