The Stacks project

Definition 7.2.1. A presheaf of sets on $\mathcal{C}$ is a contravariant functor from $\mathcal{C}$ to $\textit{Sets}$. Morphisms of presheaves are transformations of functors. The category of presheaves of sets is denoted $\textit{PSh}(\mathcal{C})$.

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View Definition 7.2.1 as pdf