The Stacks project

Definition 35.36.1. Let $\mathcal{P}$ be a property of morphisms of schemes over a base. Let $\tau \in \{ Zariski, fpqc, fppf, {\acute{e}tale}, smooth, syntomic\} $. We say morphisms of type $\mathcal{P}$ satisfy descent for $\tau $-coverings if for any $\tau $-covering $\mathcal{U} : \{ U_ i \to S\} _{i \in I}$ (see Topologies, Section 34.2), any descent datum $(X_ i, \varphi _{ij})$ relative to $\mathcal{U}$ such that each morphism $X_ i \to U_ i$ has property $\mathcal{P}$ is effective.