Lemma 92.20.4 (08UW)—The Stacks project

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Table of contents
Part 6: Deformation Theory
Chapter 92: The Cotangent Complex
Section 92.20: The cotangent complex of a morphism of ringed spaces
Lemma 92.20.4 (cite)

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Lemma 92.20.4. Let $f : (X, \mathcal{O}_ X) \to (Y, \mathcal{O}_ Y)$ be a morphism of ringed spaces. There is a canonical map $L_{X/Y} \to \mathop{N\! L}\nolimits _{X/Y}$ which identifies the naive cotangent complex with the truncation $\tau _{\geq -1}L_{X/Y}$ .

Proof. Special case of Lemma 92.18.10. $\square$

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