Fill in the blank, please :)

Let $\mathcal C$ be a complete and cocomplete abelian category. A

generatorin $\mathcal C$ is an object $X \in \mathcal C$ such that every object $Y \in \mathcal C$ is acolimitof a (small) diagram made entirely of $X$s; in this way, $X$ knows everything there is to know about $\mathcal C$. When $\mathcal C$ is the category of all modules of some ring $R$, then an example of a generator is $R$, thought of as an $R$-module. Acogeneratorin $\mathcal C$ is an object $X \in \mathcal C$ such that every object $Y \in \mathcal C$ is alimitof a (small) diagram made entirely of $X$s; in this way, $X$ knows everything there is to know about $\mathcal C$. When $\mathcal C$ is the category of all modules of some ring $R$, then an example of a cogenerator is`________`

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The only examples I know are: when $R = \mathbb Z$, an example of a cogenerator is the rational circle $\mathbb Q / \mathbb Z$; when $R = \mathbb K$ is a field, an example of a cogenerator is $\mathbb K$. But by some version of the Law of Small Numbers, these examples are not enough for me to see how to (or, in fact, whether it is possible to) generalize.