Connect Object - Connected Scheme

Algebraic Geometry
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Tsakanikas Nickos
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Connect Object - Connected Scheme

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Post by Tsakanikas Nickos »

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.
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