Cancellation law for étale morphisms

Lemma 29.36.18. Let $f : X \to Y$ be a morphism of schemes over $S$. If $X$ and $Y$ are étale over $S$, then $f$ is étale.

Proof. See Algebra, Lemma 10.142.8. $\square$

Comment #3037 by Brian Lawrence on

Suggested slogan: A map between two schemes, which are etale over a common base, is etale.

Comment #4953 by awllower on

Suggested slogan: Cancellation law for étale morphisms.

Comment #4971 by Floris Ruijter on

Suggested slogan: Morphism of étale schemes is étale.

Comment #5209 by on

OK, I went with the cancellation law slogan

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