The Stacks project

Definition 76.21.1. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. The naive cotangent complex of $f$ is the complex defined in Modules on Sites, Definition 18.35.4 for the morphism of ringed topoi $f_{small}$ between the small étale sites of $X$ and $Y$, see Properties of Spaces, Lemma 66.21.3. Notation: $\mathop{N\! L}\nolimits _ f$ or $\mathop{N\! L}\nolimits _{X/Y}$.

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