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A map of rings $f:A\to B$ is called "essentially $P$" if there exists some $A\to C\to B$ such that $A\to C$ has property $P$ and $C\to B$ is a localization, that is to say, a filtered colimit of Zariski-open $C$-algebras.

Is there a name for a map $A\to B$ such that there exists a factorization $A\to C\to B$ such that $A\to C$ has property $P$ and $C\to B$ is a strict localization, that is to say, a filtered colimit of étale $C$-algebras?

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