Definition mor_preserves_opcartesian_to_mor_preserves_cartesian {B : bicat} {e₁ b₁ : B} {p₁ : e₁ --> b₁} {e₂ b₂ : B} {p₂ : e₂ --> b₂} {fe : e₁ --> e₂} (H : mor_preserves_opcartesian p₁ p₂ fe) : @mor_preserves_cartesian (op2_bicat B) e₁ b₁ p₁ e₂ b₂ p₂ fe. Proof. intros x f g γ Hγ. apply is_opcartesian_to_is_cartesian_sfib. apply H. apply is_cartesian_to_is_opcartesian_sfib. exact Hγ. 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.Core.Univalence. Require Import UniMath.Bicategories.Core.UnivalenceOp. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration.