proposition: Lemma functor_full_img_is_unitarily_eso : is_unitarily_eso functor_full_img_is_dagger_functor.
proof: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Subcategory.Core UniMath.CategoryTheory.Subcategory.Full UniMath.CategoryTheory.DaggerCategories.Categories UniMath.CategoryTheory.DaggerCategories.Unitary UniMath.CategoryTheory.DaggerCategories.Univalence UniMath.CategoryTheory.DaggerCategories.Functors UniMath.CategoryTheory.DaggerCategories.Functors.WeakEquivalences UniMath.CategoryTheory.DaggerCategories.Examples.Fullsub