Definition 90.20.1. Let $f : (X, \mathcal{O}_ X) \to (S, \mathcal{O}_ S)$ be a morphism of ringed spaces. The *cotangent complex* $L_ f$ of $f$ is $L_ f = L_{\mathcal{O}_ X/f^{-1}\mathcal{O}_ S}$. We will also use the notation $L_ f = L_{X/S} = L_{\mathcal{O}_ X/\mathcal{O}_ S}$.

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