Definition fully_faithful_reflect_dagger_structure {C D : category} {F : functor C D} (dagD : dagger D) (ff : fully_faithful F) : dagger_structure C. Proof. intros x y f. apply (fully_faithful_inv_hom ff y x). exact (pr1 dagD _ _ (#F f)). 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. Require Import UniMath.CategoryTheory.DaggerCategories.Functors. Require Import UniMath.CategoryTheory.DaggerCategories.Unitary.