Definition 17.31.1. Let X be a topological space. Let \mathcal{A} \to \mathcal{B} be a homomorphism of sheaves of rings. The naive cotangent complex \mathop{N\! L}\nolimits _{\mathcal{B}/\mathcal{A}} is the chain complex (17.31.0.2)
with \mathcal{I}/\mathcal{I}^2 placed in degree -1 and \Omega _{\mathcal{A}[\mathcal{B}]/\mathcal{A}} \otimes _{\mathcal{A}[\mathcal{B}]} \mathcal{B} placed in degree 0.
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