The Stacks project

Lemma 88.11.4. Consider the property $P$ on arrows of $\textit{WAdm}^{adic*}$ defined in Lemma 88.11.1. Then $P$ is stable under composition as defined in Formal Spaces, Remark 87.21.13.

Proof. The statement makes sense by Lemma 88.11.1. The easiest way to prove it is true is to show that (a) compositions of adic ring maps between adic topological rings are adic and (b) that compositions of continuous ring maps preserves the property of being topologically of finite type. We omit the details. $\square$

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