The Stacks project

Lemma 93.9.6. In Example 93.9.1 let $X$ be a scheme over $k$. Let $U \subset X$ be an open subscheme. There is a natural functor

\[ \mathcal{D}\! \mathit{ef}_ X \longrightarrow \mathcal{D}\! \mathit{ef}_ U \]

of deformation categories.

Proof. Given a deformation of $X$ we can take the corresponding open of it to get a deformation of $U$. We omit the details. $\square$

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