The Stacks project

Remark 49.2.11. Let $f : Y \to X$ be a locally quasi-finite morphism of locally Noetherian schemes. It is clear from Lemma 49.2.3 that there is a unique coherent $\mathcal{O}_ Y$-module $\omega _{Y/X}$ on $Y$ such that for every pair of affine opens $\mathop{\mathrm{Spec}}(B) = V \subset Y$, $\mathop{\mathrm{Spec}}(A) = U \subset X$ with $f(V) \subset U$ there is a canonical isomorphism

and where these isomorphisms are compatible with restriction maps.