The Stacks project

Definition 18.35.4. Let $X = (\mathop{\mathit{Sh}}\nolimits (\mathcal{C}), \mathcal{O})$ and $Y = (\mathop{\mathit{Sh}}\nolimits (\mathcal{C}'), \mathcal{O}')$ be ringed topoi. Let $(f, f^\sharp ) : X \to Y$ be a morphism of ringed topoi. The naive cotangent complex $\mathop{N\! L}\nolimits _ f = \mathop{N\! L}\nolimits _{X/Y}$ of the given morphism of ringed topoi is $\mathop{N\! L}\nolimits _{\mathcal{O}/f^{-1}\mathcal{O}'}$. We sometimes write $\mathop{N\! L}\nolimits _{X/Y} = \mathop{N\! L}\nolimits _{\mathcal{O}/\mathcal{O}'}$.