The Stacks project

Definition 60.7.1. Let $\mathcal{C}$ be a site. Let $\mathcal{O}$ be a sheaf of rings on $\mathcal{C}$. Let $\mathcal{I} \subset \mathcal{O}$ be a sheaf of ideals. A divided power structure $\gamma$ on $\mathcal{I}$ is a sequence of maps $\gamma _ n : \mathcal{I} \to \mathcal{I}$, $n \geq 1$ such that for any object $U$ of $\mathcal{C}$ the triple

is a divided power ring.