# The Stacks Project

## Tag 01AK

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}

There are no comments yet for this tag.

## Add a comment on tag 01AK

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the lower-right corner).