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## Connect Object - Connected Scheme

Algebraic Geometry
Tsakanikas Nickos
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### Connect Object - Connected Scheme

Let $X$ be a scheme and let $\mathcal{FÉt}_{X}$ be the category of finite étale schemes over $X$. Show that the following are equivalent:
1. $Y$ is a connected object in $\mathcal{FÉt}_{X}$.
2. $Y$ is connected as a scheme.