Definition is_nat_z_iso_functor_total_category_of_set_functor_on_id {C : setcategory} (F : C ⟶ cat_of_setcategory) : is_nat_z_iso (functor_total_category_of_set_functor_on_id_data F). Proof. intro. apply identity_is_z_iso. 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.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Categories.CategoryOfSetCategories. Require Import UniMath.CategoryTheory.GrothendieckConstruction.TotalCategory. Section FunctorTotalCategoryFromSetFunctor. End FunctorTotalCategoryFromSetFunctor. Section NatTransTotalCategoryFromNatTrans. End NatTransTotalCategoryFromNatTrans.