Definition PreShv_of_elems_slice_of_PreShv_equiv : equivalence_of_cats (PreShv ∫P) (PreShv C / P) := (PreShv_to_slice ,, slice_to_PreShv ,, PreShv_unit ,, slice_counit) ,, (PreShv_all_iso ,, slice_all_z_iso).
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import