Definition street_opfib_pr1_total_setcategory {C : setcategory} (G : C ⟶ cat_of_setcategory) : street_opfib (pr1_total_category_of_set_functor G). Proof. intros x y f. simple refine (_ ,, (_ ,, _) ,, _ ,, _). - exact (y ,, pr1 (#G f) (pr2 x)). - exact (f ,, identity _). - apply identity_z_iso. - exact (!(id_right f)). - apply is_opcartesian_total_setcategory_of_set_functor. apply is_z_isomorphism_identity. 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.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.DisplayedCats.StreetOpFibration. Require Import UniMath.CategoryTheory.Categories.CategoryOfSetCategories. Require Import UniMath.CategoryTheory.GrothendieckConstruction.TotalCategory. Require Import UniMath.CategoryTheory.GrothendieckConstruction.Projection.