The Stacks project

Definition 17.29.4. Let $X$ be a topoological space. Let $\mathcal{O}_1 \to \mathcal{O}_2$ be a map of sheaves of rings on $X$. Let $\mathcal{F}$ be a sheaf of $\mathcal{O}_2$-modules. The module $\mathcal{P}^ k_{\mathcal{O}_2/\mathcal{O}_1}(\mathcal{F})$ constructed in Lemma 17.29.3 is called the module of principal parts of order $k$ of $\mathcal{F}$.