Definition 22.26.1 (09L5)—The Stacks project

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Part 1: Preliminaries
Chapter 22: Differential Graded Algebra
Section 22.26: Differential graded categories
Definition 22.26.1 (cite)

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Definition 22.26.1. Let $R$ be a ring. A differential graded category $\mathcal{A}$ over $R$ is a category where every morphism set is given the structure of a differential graded $R$ -module and where for $x, y, z \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{A})$ composition is $R$ -bilinear and induces a homomorphism

$\mathop{\mathrm{Hom}}\nolimits _\mathcal {A}(y, z) \otimes _ R \mathop{\mathrm{Hom}}\nolimits _\mathcal {A}(x, y) \longrightarrow \mathop{\mathrm{Hom}}\nolimits _\mathcal {A}(x, z)$

of differential graded $R$ -modules.

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