Definition nat_trans_total_category_of_set_functor_eq (x : total_precategory_of_set_functor G₁) : pr1 (# G₂ (α (pr1 x))) (pr1 (pr1 β₁ (pr1 x)) (pr2 x)) = pr1 (pr1 β₂ (pr1 x)) (pr2 x).
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.