proposition: Lemma Precomp_of_dagger_weak_equiv_is_dagger_weak_equiv {C D E : category} {dagC : dagger C} {dagD : dagger D} {H : functor C D} {dagH : is_dagger_functor dagC dagD H} (wH : is_weak_dagger_equiv dagH) {dagE : dagger E} (univE : is_univalent_dagger dagE) : is_weak_dagger_equiv (dagger_pre_composition_functor_is_dagger_functor dagH dagE).
proof: Proof. split. - exact (Precomp_is_unitarily_eso _ wH univE). - exact (Precomp_is_ff _ 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