Remark 2.3.1.19. Let $G$ be a monoid, regarded as a monoidal category having only identity morphisms. Then the classifying simplicial set $B_{\bullet }G$ of Example 2.3.1.18 agrees (up to canonical isomorphism) with the simplicial set $B_{\bullet }G$ given by the Milnor construction, described in Example 1.2.4.3.

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