## Tag `08WQ`

Chapter 34: Descent > Section 34.4: Descent for universally injective morphisms

Definition 34.4.9. Let $R$ be a ring. Define the contravariant functor

$C$$ : \text{Mod}_R \to \text{Mod}_R$ by setting $$ C(M) = \mathop{\rm Hom}\nolimits_{\textit{Ab}}(M, \mathbf{Q}/\mathbf{Z}), $$ with the $R$-action on $C(M)$ given by $rf(s) = f(rs)$.

The code snippet corresponding to this tag is a part of the file `descent.tex` and is located in lines 942–950 (see updates for more information).

```
\begin{definition}
\label{definition-C}
Let $R$ be a ring. Define the contravariant functor
{\it $C$} $ : \text{Mod}_R \to \text{Mod}_R$ by setting
$$
C(M) = \Hom_{\textit{Ab}}(M, \mathbf{Q}/\mathbf{Z}),
$$
with the $R$-action on $C(M)$ given by $rf(s) = f(rs)$.
\end{definition}
```

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