Definition sheaf_locality_ax : UU := ∏ (c : C) (S : covering_sieve c) (f g : (P c : hSet)), (∏ (h : sieve_selected_morphism S), # P h f = # P h g) → f = g.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.Notations. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Limits. Require Import UniMath.CategoryTheory.Categories.HSET.Univalence. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions.FullSubcategory. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Presheaf. Require Import UniMath.CategoryTheory.yoneda. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.GrothendieckToposes.Sieves. Require Import UniMath.CategoryTheory.GrothendieckToposes.Sites.