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Definition 4.3.3. Let $\mathcal{C}$ be a category.

  1. A presheaf of sets on $\mathcal{C}$ or simply a presheaf is a contravariant functor $F$ from $\mathcal{C}$ to $\textit{Sets}$.

  2. The category of presheaves is denoted $\textit{PSh}(\mathcal{C})$.

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