Remark 4.3.3.14. For every pair of simplicial sets $X$ and $Y$, we have canonical monomorphisms

\[ X \simeq X \star \emptyset \hookrightarrow X \star Y \hookleftarrow \emptyset \star Y \simeq Y. \]

We will often abuse notation by identifying $X$ and $Y$ with the simplicial subsets of $X \star Y$ given by the images of these monomorphisms.