Definition 10.133.1. Let $R \to S$ be a ring map. The *naive cotangent complex* $\mathop{N\! L}\nolimits _{S/R}$ is the chain complex (10.133.0.2)

with $I/I^2$ placed in (homological) degree $1$ and $\Omega _{R[S]/R} \otimes _{R[S]} S$ placed in degree $0$. We will denote $H_1(L_{S/R}) = H_1(\mathop{N\! L}\nolimits _{S/R})$^{1} the homology in degree $1$.

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