Remark 24.22.5. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. Let $\mathcal{A}$ be a sheaf of differential graded algebras on $(\mathcal{C}, \mathcal{O})$. Let $C = C(\text{id}_\mathcal {A})$ be the cone on the identity map $\mathcal{A} \to \mathcal{A}$ viewed as a map of differential graded $\mathcal{A}$-modules. Then

$\mathop{\mathrm{Hom}}\nolimits _{\textit{Mod}(\mathcal{A}, \text{d})}(C, \mathcal{M}) = \{ (x, y) \in \Gamma (\mathcal{C}, \mathcal{M}^0) \times \Gamma (\mathcal{C}, \mathcal{M}^{-1}) \mid x = \text{d}(y)\}$

where the map from left to right sends $f$ to the pair $(x, y)$ where $x$ is the image of the global section $(0, 1)$ of $C^{-1} = \mathcal{A}^{-1} \oplus \mathcal{A}^0$ and where $y$ is the image of the global section $(1, 0)$ of $C^0 = \mathcal{A}^0 \oplus \mathcal{A}^1$.

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