Definition is_setcategory_total_of_set_functor {C : setcategory} (F : C ⟶ cat_of_setcategory) : is_setcategory (total_precategory_of_set_functor F). Proof. split. - apply isaset_total2. + apply C. + intro. apply (F x). - intros x y. apply isaset_total2. + apply homset_property. + intro. apply homset_property. 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.Categories.CategoryOfSetCategories.