Definition fully_faithful_is_dagger_functor {C D : category} {F : functor C D} (dagD : dagger D) (ff : fully_faithful F) : is_dagger_functor (fully_faithful_reflect_dagger dagD ff) dagD F.
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.