Expanding upon Remark 2.5.1.1.2, Remark 2.5.2.1.2, and Remark 2.5.3.1.2, we may view the characteristic embedding
\[ \chi _{\webleft (-\webright )}\colon X\hookrightarrow \mathcal{P}\webleft (X\webright ) \]
of $X$ into $\mathcal{P}\webleft (X\webright )$ as a decategorification of the Yoneda embedding
\[ {\text{よ}}\colon \mathcal{C}^{\mathsf{op}} \hookrightarrow \mathsf{PSh}\webleft (\mathcal{C}\webright ) \]
of a category $\mathcal{C}$ into $\mathsf{PSh}\webleft (\mathcal{C}\webright )$.
