The Stacks project

Remark 87.21.8 (Variant for adic-star). Let $P$ be a local property of morphisms of $\textit{WAdm}^{adic*}$, see Remark 87.21.4. We say $P$ is stable under base change if given $B \to A$ and $B \to C$ in $\textit{WAdm}^{adic*}$ we have $P(B \to A) \Rightarrow P(C \to A \widehat{\otimes }_ B C)$. This makes sense as $A \widehat{\otimes }_ B C$ is an object of $\textit{WAdm}^{adic*}$ by Lemma 87.4.12. In exactly the same way we obtain a variant of Lemma 87.21.7 for morphisms between locally adic* formal algebraic spaces over $S$.