Remark 8.1.0.6. Let $\operatorname{\mathcal{C}}$ be a category. For every object $X \in \operatorname{\mathcal{C}}$, the fiber $\{ X\} \times _{ \operatorname{\mathcal{C}}^{\operatorname{op}} } \operatorname{Tw}(\operatorname{\mathcal{C}})$ can be identified with the coslice category $\operatorname{\mathcal{C}}_{X/}$ of Variant 4.3.1.4. Similarly, the fiber $\operatorname{Tw}(\operatorname{\mathcal{C}}) \times _{\operatorname{\mathcal{C}}} \{ X\} $ can be identified with the opposite of the slice category $\operatorname{\mathcal{C}}_{/X}$ of Construction 4.3.1.1.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$