Definition 88.15.4. Let $\varphi : A \to B$ be a continuous ring homomorphism between adic Noetherian topological rings, i.e., $\varphi $ is an arrow of $\textit{WAdm}^{Noeth}$. We say $\varphi $ is rig-flat if $\varphi $ is adic, topologically of finite type, and for all $f \in A$ the induced map
\[ A_{\{ f\} } \longrightarrow B_{\{ f\} } \]
is naively rig-flat (Definition 88.15.2).
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