The Stacks project

Definition 96.3.1. Let $p : \mathcal{X} \to (\mathit{Sch}/S)_{fppf}$ be a category fibred in groupoids.

1. A presheaf on $\mathcal{X}$ is a presheaf on the underlying category of $\mathcal{X}$.

2. A morphism of presheaves on $\mathcal{X}$ is a morphism of presheaves on the underlying category of $\mathcal{X}$.

We denote $\textit{PSh}(\mathcal{X})$ the category of presheaves on $\mathcal{X}$.