proposition: Lemma comp_essentially_surjective {B1 B2 B3 : bicat} {F : psfunctor B1 B2} {G : psfunctor B2 B3} (Feso : essentially_surjective_psfunctor F) (Geso : essentially_surjective_psfunctor G) : essentially_surjective_psfunctor (comp_psfunctor G F).
proof: Proof. intro z. use (factor_through_squash_hProp _ _ (Geso z)). intros [y yp]. use (factor_through_squash_hProp _ _ (Feso y)). intros [x xp]. apply hinhpr. exists x. use (Composition.comp_adjequiv _ yp). use (psfunctor_preserve_adj_equiv G). exact xp. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.CompositesAndInverses UniMath.CategoryTheory.PrecompEquivalence UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.RezkCompletion UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.YonedaLemma UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat UniMath.Bicategories.PseudoFunctors.PseudoFunctor UniMath.Bicategories.PseudoFunctors.Properties UniMath.Bicategories.PseudoFunctors.Examples.Composition