proposition: Lemma comp_local_weak_equivalence {B1 B2 B3 : bicat} {F : psfunctor B1 B2} {G : psfunctor B2 B3} (Feso : local_weak_equivalence F) (Geso : local_weak_equivalence G) : local_weak_equivalence (comp_psfunctor G F).
proof: Proof. intros x y. split. - use (comp_essentially_surjective (Fmor F x y) _ (Fmor G _ _)). + exact (pr1 (Feso x y)). + apply (pr1 (Geso _ _)). - use (comp_ff_is_ff _ _ _ (Fmor F x y) _ (Fmor G _ _)). + exact (pr2 (Feso x y)). + apply (pr2 (Geso _ _)). Defined.
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