Transitivity Triangle Cotangent Complex

Lemma

Let \(X\xrightarrow{f}Y\xrightarrow{g}Z\) be morphisms of schemes or algebraic stacks. Then there is a canonical distinguished “transitivity triangle”

\begin{align*} f^*L_{Y/Z} \to L_{X/Z} \to L_{X/Y} \xrightarrow{+1}... \end{align*}

of relative cotangent complexes.