Definition 92.22.1. Let $(f, f^\sharp ) : (\mathop{\mathit{Sh}}\nolimits (\mathcal{C}), \mathcal{O}_\mathcal {C}) \to (\mathop{\mathit{Sh}}\nolimits (\mathcal{D}), \mathcal{O}_\mathcal {D})$ be a morphism of ringed topoi. The *cotangent complex* $L_ f$ of $f$ is $L_ f = L_{\mathcal{O}_\mathcal {C}/f^{-1}\mathcal{O}_\mathcal {D}}$. We sometimes write $L_ f = L_{\mathcal{O}_\mathcal {C}/\mathcal{O}_\mathcal {D}}$.

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