Definition 35.4.9 (08WQ)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 35: Descent
Section 35.4: Descent for universally injective morphisms
Definition 35.4.9 (cite)

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Definition 35.4.9. Let $R$ be a ring. Define the contravariant functor $C$ $: \text{Mod}_ R \to \text{Mod}_ R$ by setting

$C(M) = \mathop{\mathrm{Hom}}\nolimits _{\textit{Ab}}(M, \mathbf{Q}/\mathbf{Z}),$

with the $R$ -action on $C(M)$ given by $rf(s) = f(rs)$ .

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