The Stacks project

Lemma 6.27.2. Let $X$ be a topological space, $x \in X$ a point, and $A$ a set. For any point $x' \in X$ the stalk of the skyscraper sheaf at $x$ with value $A$ at $x'$ is

\[ (i_{x, *}A)_{x'} = \left\{ \begin{matrix} A & \text{if} & x' \in \overline{\{ x\} } \\ \{ *\} & \text{if} & x' \not\in \overline{\{ x\} } \end{matrix} \right. \]

A similar description holds for the case of abelian groups, algebraic structures and sheaves of modules.

Proof. Omitted. $\square$

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