## Tag `01AK`

Chapter 17: Sheaves of Modules > Section 17.3: The abelian category of sheaves of modules

Lemma 17.3.4. Let $j : U \to X$ be an open immersion of topological spaces. The functor $j_! : \textit{Ab}(U) \to \textit{Ab}(X)$ is exact.

Proof.Follows from the description of stalks given in Sheaves, Lemma 6.31.6. $\square$

The code snippet corresponding to this tag is a part of the file `modules.tex` and is located in lines 280–285 (see updates for more information).

```
\begin{lemma}
\label{lemma-j-shriek-exact}
Let $j : U \to X$ be an open immersion of topological spaces.
The functor $j_! : \textit{Ab}(U) \to \textit{Ab}(X)$
is exact.
\end{lemma}
\begin{proof}
Follows from the description of stalks
given in Sheaves, Lemma \ref{sheaves-lemma-j-shriek-abelian}.
\end{proof}
```

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