$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Remark Let $\operatorname{\mathcal{C}}$ be an ordinary category and let $\underline{\operatorname{\mathcal{C}}}$ denote the associated constant simplicial category (Example Then the simplicial categories $\underline{\operatorname{\mathcal{C}}}^{\triangleleft }$ and $\underline{\operatorname{\mathcal{C}}}^{\triangleright }$ of Notation and Variant are also constant, associated to the ordinary categories $\operatorname{\mathcal{C}}^{\triangleleft }$ and $\operatorname{\mathcal{C}}^{\triangleright }$ of Example In other words, the formation of cones is compatible with the operation of regarding an ordinary category as a (constant) simplicial category.