Definition pr1_total_category_of_set_functor {C : setcategory} (F : C ⟶ cat_of_setcategory) : total_setcategory_of_set_functor F ⟶ C. Proof. use make_functor. - exact (pr1_total_category_of_set_functor_data F). - exact (pr1_total_category_of_set_is_functor F). 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.