Definition street_opfib_is_internal_sopfib_opcleaving_lift_data : functor_data (pr1 C₀) (pr1 C₁). Proof. use make_functor_data. - exact (λ x, pr1 (HF _ _ (pr1 α x))). - intros x y f ; cbn. use (opcartesian_factorization_sopfib _ (pr222 (HF _ _ (pr1 α x)))). + exact (# (pr1 G₁) f · pr112 (HF _ _ (pr1 α y))). + exact (inv_from_z_iso (pr212 (HF _ _ (pr1 α x))) · # (pr1 G₂) f · pr212 (HF _ _ (pr1 α y))). + abstract (rewrite functor_comp ; rewrite (pr122 (HF _ _ (pr1 α x))) ; refine (maponpaths (λ z, _ · z) (pr122 (HF _ _ (pr1 α y))) @ _) ; rewrite !assoc ; apply maponpaths_2 ; refine (nat_trans_ax α _ _ f @ _) ; rewrite !assoc' ; apply maponpaths ; rewrite !assoc ; rewrite z_iso_inv_after_z_iso ; rewrite id_left ; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.DisplayedCats.StreetFibration. Require Import UniMath.CategoryTheory.DisplayedCats.StreetOpFibration. 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.Univalence. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration. Require Import UniMath.Bicategories.Morphisms.InternalStreetOpFibration.