Definition pb_lwhisker_is_cartesian : lwhisker_is_cartesian p₁. Proof. intros x y h f g α Hα. apply to_pb_cartesian. use is_cartesian_eq. - exact (rassociator _ _ _ • (h ◃ (α ▹ fe)) • lassociator _ _ _). - abstract (rewrite rwhisker_lwhisker_rassociator ; rewrite !vassocl ; rewrite rassociator_lassociator ; apply id2_right). - use vcomp_is_cartesian_2cell_sfib. + use vcomp_is_cartesian_2cell_sfib. * apply invertible_is_cartesian_2cell_sfib. is_iso. * apply (pr2 Hf). apply from_pb_cartesian. exact Hα. + apply invertible_is_cartesian_2cell_sfib. is_iso. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Examples.OpCellBicat. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.DiscreteMorphisms. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration. Require Import UniMath.Bicategories.Morphisms.InternalStreetOpFibration. Require Import UniMath.Bicategories.Morphisms.Properties.Composition. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.Examples.OpCellBicatLimits. Section FromPBCartesian. End FromPBCartesian.