Lemma 22.19.10. Let $R$ be a ring. Let $\mathcal{A}$ be a differential graded category over $R$. Let $x$ be an object of $\mathcal{A}$. Let

be the differential graded $R$-algebra of endomorphisms of $x$. We obtain a functor

of differential graded categories by letting $E$ act on $\mathop{\mathrm{Hom}}\nolimits _\mathcal {A}(x, y)$ via composition in $\mathcal{A}$. This functor induces functors

by an application of Lemma 22.19.5.

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