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Homotopy limit over a diagram of nullhomotopic maps
Let $I$ be a $\mathrm{Top}_*$-enriched poset and $X: I \to \mathrm{Top}_*$, and consider the homotopy limit
$$
\underset{i \in I}{\mathrm{holim}}X(i),
$$
where the maps $X(i) \to X(j)$ are nullhomoto …