Remark 4.7.4.7. Let $S$ be a simplicial set. Then there is a least infinite cardinal $\kappa $ for which $S$ is $\kappa $-small. If $S$ is finite, then $\kappa = \aleph _0$. If $S$ is not finite, then $\kappa = \lambda ^{+}$, where $\lambda $ is the cardinality of the set of all nondegenerate simplices of $S$. In particular, $\kappa $ is always a regular cardinal.
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