The Stacks project

Remark 87.21.14 (Variant for Noetherian). Let $P$ be a local property of morphisms of $\textit{WAdm}^{Noeth}$, see Remark 87.21.5. We say $P$ is stable under composition if given $B \to A$ and $C \to B$ in $\textit{WAdm}^{Noeth}$ we have $P(B \to A) \wedge P(C \to B) \Rightarrow P(C \to A)$. In exactly the same way we obtain a variant of Lemma 87.21.12 for morphisms between locally Noetherian formal algebraic spaces over $S$.