The Stacks project

Definition 91.26.1. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. The cotangent complex $L_{X/Y}$ of $X$ over $Y$ is the cotangent complex of the morphism of ringed topoi $f_{small}$ between the small ├ętale sites of $X$ and $Y$ (see Properties of Spaces, Lemma 65.21.3 and Definition 91.22.1).

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