Lemma functor_full_img_is_unitarily_eso : is_unitarily_eso functor_full_img_is_dagger_functor. Proof. intro d. use (factor_through_squash_hProp _ _ (pr2 d)). intro c. apply hinhpr. exists (pr1 c). exists (pr12 c ,, tt). split ; (use subtypePath ; [intro ; apply isapropunit |]) ; apply (pr2 c). 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.