Definition comp_conservative {B : bicat} {a b c : B} {f : a --> b} {g : b --> c} (Hf : conservative_1cell f) (Hg : conservative_1cell g) : conservative_1cell (f · g). Proof. intros x g₁ g₂ α Hα. apply Hf. apply Hg. use eq_is_invertible_2cell. - exact (rassociator _ _ _ • (α ▹ f · g) • lassociator _ _ _). - abstract (rewrite !vassocl ; rewrite <- rwhisker_rwhisker ; rewrite !vassocr ; rewrite rassociator_lassociator ; apply id2_left). - use is_invertible_2cell_vcomp. + use is_invertible_2cell_vcomp. * is_iso. * exact Hα. + is_iso. 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.