proposition: Lemma Precomp_is_ff : fully_faithful (dagger_pre_composition_functor dagH dagE).
proof: Proof. use (disp_functor_ff_to_total_ff _ disp_dagger_pre_composition_functor_ff). apply pre_composition_with_ess_surj_and_full_is_fully_faithful. - exact (is_unitarily_eso_is_eso _ (pr1 wH)). - exact (pr1 (fully_faithful_implies_full_and_faithful _ _ _ (pr2 wH))). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.TotalCategoryFacts UniMath.CategoryTheory.precomp_fully_faithful UniMath.CategoryTheory.DaggerCategories.Categories UniMath.CategoryTheory.DaggerCategories.Functors UniMath.CategoryTheory.DaggerCategories.Transformations UniMath.CategoryTheory.DaggerCategories.Unitary UniMath.CategoryTheory.DaggerCategories.Univalence UniMath.CategoryTheory.DaggerCategories.FunctorCategory UniMath.CategoryTheory.DaggerCategories.Functors.FullyFaithful UniMath.CategoryTheory.DaggerCategories.Functors.WeakEquivalences