Definition comp_lwhisker_is_cartesian : lwhisker_is_cartesian (f · g). Proof. intros x y h k₁ k₂ γ Hγ. use to_is_cartesian_2cell_comp. - apply (pr2 Hf). exact (from_is_cartesian_2cell_comp _ Hγ). - assert (((h ◃ γ) ▹ f) • rassociator _ _ _ = rassociator _ _ _ • (h ◃ (γ ▹ f))) as r. { abstract (rewrite rwhisker_lwhisker_rassociator ; apply idpath). } refine (is_cartesian_2cell_sfib_postcomp _ ((h ◃ γ) ▹ f) _ _ r). + apply invertible_is_cartesian_2cell_sfib. is_iso. + use vcomp_is_cartesian_2cell_sfib. * apply invertible_is_cartesian_2cell_sfib. is_iso. * apply Hg. apply from_is_cartesian_2cell_comp_rwhisker. exact Hγ. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.DiscreteMorphisms. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration. Require Import UniMath.Bicategories.Morphisms.InternalStreetOpFibration. Section FromCompCartesian. End FromCompCartesian.