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A simplicial presheaf is a presheaf on a site (e.g., the category of topological spaces) taking values in simplicial sets (i.e., a contravariant functor from the site to the category of simplicial sets).

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Slice category of simplicial presheaves

If $\mathcal{C}$ is a small category and we let $\mathbf{Pre}(\mathcal{C})$ denote the category of presheaves over $\mathcal{C}$, then it is well known that for any presheaf $X \in \mathbf{Pre}(\mathc …
Emilio Minichiello's user avatar