Definition 91.19.1. Let $\mathcal{C}$ be a site. Let $\mathcal{A} \to \mathcal{B}$ be a homomorphism of sheaves of rings. Let $\mathcal{F}$ be a sheaf of $\mathcal{B}$-modules. The map $\mathcal{F} \to L_{\mathcal{B}/\mathcal{A}} \otimes _\mathcal {B}^\mathbf {L} \mathcal{F}[1]$ in (91.19.0.2) is called the Atiyah class of $\mathcal{F}$.

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