Definition 25.2.2. Let $\mathcal{C}$ be a category. We denote $F$ the functor which associates a presheaf to a semi-representable object. In a formula

\begin{eqnarray*} F : \text{SR}(\mathcal{C}) & \longrightarrow & \textit{PSh}(\mathcal{C}) \\ \{ U_ i\} _{i \in I} & \longmapsto & \amalg _{i\in I} h_{U_ i} \end{eqnarray*}

where $h_ U$ denotes the representable presheaf associated to the object $U$.

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