# The Stacks Project

## Tag 01DA

Lemma 15.52.6. Let $R$ be a ring. The functor $M \mapsto M^\vee$ is exact.

Proof. This because $\mathbf{Q}/\mathbf{Z}$ is an injective abelian group by Lemma 15.51.1. $\square$

The code snippet corresponding to this tag is a part of the file more-algebra.tex and is located in lines 12142–12146 (see updates for more information).

\begin{lemma}
\label{lemma-vee-exact}
Let $R$ be a ring.
The functor $M \mapsto M^\vee$ is exact.
\end{lemma}

\begin{proof}
This because $\mathbf{Q}/\mathbf{Z}$
is an injective abelian group by Lemma \ref{lemma-injective-abelian}.
\end{proof}

There are no comments yet for this tag.

There are also 4 comments on Section 15.52: More on Algebra.

## Add a comment on tag 01DA

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).