More generally, let X \to Y is a Deligne-Mumford Type (DM-type) morphism of Artin Stacks which is locally of finite type. Then \mathfrak{C}_{X/Y} \subseteq \mathfrak{N}_{X/Y} is characterised as the closed substack such that, for any étale map U \to X for which U \to X \to Y factors through some smooth map M \to Y (e.g., \mathbb{A}_Y^n \to Y), the pullback is:
