Remark 3.3.3.6. Let $X$ be a finite simplicial set. Then the subdivision $\operatorname{Sd}(X)$ is also finite. By virtue of Proposition 3.6.1.7, it suffices to prove this in the case where $X = \Delta ^ n$ is a standard simplex, in which case it follows from the explicit description given in Example 3.3.3.5.
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