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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).

5 votes

Is there a practical criterion to determine whether the limit of a diagram of real chain com...

Since all your complexes are concentrated in a fixed degree $n$, the cohomology of the homotopy limit is $H^{n+r}(\operatorname{holim}D)=\lim^rD^n$, hence a criterion would be the vanishing of higher …
Fernando Muro's user avatar