The Stacks project

Definition 92.26.1. 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 étale sites of $X$ and $Y$ (see Properties of Spaces, Lemma 66.21.3 and Definition 92.22.1).