# Kerodon

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

Example 6.2.2.5. Let $\operatorname{\mathcal{C}}$ be an $\infty$-category which contains a final object, and let $\operatorname{\mathcal{C}}^{\mathrm{fin}}$ denote the full subcategory of $\operatorname{\mathcal{C}}$ spanned by its final objects (so that $\operatorname{\mathcal{C}}^{\mathrm{fin}}$ is a contractible Kan complex: see Corollary 4.6.6.15). Then $\operatorname{\mathcal{C}}^{\mathrm{fin}}$ is a reflective subcategory of $\operatorname{\mathcal{C}}$.