Remark 6.3.7.11. Let $S$ and $T$ be nonsingular simplicial sets. Then the join $S \star T$ is nonsingular. In particular, if $S$ is nonsingular, then the cone $S^{\triangleright }$ is also nonsingular.
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Remark 6.3.7.11. Let $S$ and $T$ be nonsingular simplicial sets. Then the join $S \star T$ is nonsingular. In particular, if $S$ is nonsingular, then the cone $S^{\triangleright }$ is also nonsingular.