Kerodon

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Definition 1.1.3.9. Let $S_{\bullet }$ be a simplicial set and let $k \geq -1$ be an integer. We will say that $S_{\bullet }$ has dimension $\leq k$ if, for $n > k$, every $n$-simplex of $S_{\bullet }$ is degenerate. If $k \geq 0$, we say that $S_{\bullet }$ has dimension $k$ if it has dimension $\leq k$ but does not have dimension $\leq k-1$. We say that $S_{\bullet }$ is finite-dimensional if it has dimension $\leq k$ for some $k \gg 0$.