Lemma is_functor_full_dagger_img : is_functor full_dagger_img_functor_data. Proof. split. - intro ; apply subtypePath. { intro; apply isapropunit. } apply functor_id. - intro ; intros ; apply subtypePath. { intro ; apply isapropunit. } apply functor_comp. 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.Core.Isos. Require Import UniMath.CategoryTheory.Subcategory.Core. Require Import UniMath.CategoryTheory.Subcategory.Full. 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.Functors.WeakEquivalences. Require Import UniMath.CategoryTheory.DaggerCategories.Examples.Fullsub.