Definition is_cartesian_weq_is_opcartesian_sfib {B : bicat} {e b : B} {p : e --> b} {x : B} {f g : x --> e} (α : f ==> g) : @is_cartesian_2cell_sfib (op2_bicat B) e b p x g f α ≃ is_opcartesian_2cell_sopfib p α. Proof. use weqimplimpl. - exact is_cartesian_to_is_opcartesian_sfib. - exact is_opcartesian_to_is_cartesian_sfib. - apply isaprop_is_cartesian_2cell_sfib. - apply isaprop_is_opcartesian_2cell_sopfib. 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.