proposition: Lemma psfunctor_B_to_LRB_laws : psfunctor_laws psfunctor_B_to_LRB_data.
proof: Proof. repeat split. - exact (λ x y f, functor_id (η_{x,y}) f). - intros x y f g h α β. apply (functor_comp (η_{x,y})). - exact (λ x y f, prewhisker_LRB_lunitor f). - exact (λ x y f, prewhisker_LRB_runitor f). - exact (λ x y z w f g h, prewhisker_LRB_associator f g h). - intro ; intros. set (t := λ fg, ! pr21 (LRB_composition_comm a b c) (make_catbinprod (C:=hom _ _) (D:=hom _ _) f g₁) (make_catbinprod (C:=hom _ _) (D:=hom _ _) f g₂) fg). cbn in t. refine (_ @ t (catbinprodmor (C:=hom _ _) (D:=hom _ _) (id2 f) η0) @ _). + do 2 apply maponpaths. apply lwhisker_hcomp. + now rewrite (functor_id (η (hom a b))). - intro ; intros. unfold psfunctor_B_to_LRB_data. set (t := λ fg, ! pr21 (LRB_composition_comm a b c) (make_catbinprod (C:=hom _ _) (D:=hom _ _) f₁ g) (make_catbinprod (C:=hom _ _) (D:=hom _ _) f₂ g) fg). cbn in t. refine (_ @ t (catbinprodmor (C:=hom _ _) (D:=hom _ _) η0 (id2 g)) @ _). + do 2 apply maponpaths. apply rwhisker_hcomp. + now rewrite (functor_id (η (hom b c))). 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