Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Remark 8.1.5.5. Let $\operatorname{\mathcal{C}}$ be a $2$-category containing objects $X$ and $Y$. For every category $\operatorname{\mathcal{A}}$, we can use Theorem 2.3.4.1 to identify strictly unitary lax functors $U: [1] \times \operatorname{\mathcal{A}}\rightarrow \operatorname{\mathcal{C}}$ with morphisms of simplicial sets $G: \Delta ^1 \times \operatorname{N}_{\bullet }(\operatorname{\mathcal{A}}) \rightarrow \operatorname{N}_{\bullet }^{\operatorname{D}}(\operatorname{\mathcal{C}})$. Consequently, Theorem 8.1.5.4 supplies a bijection

\[ \xymatrix@R =50pt@C=50pt{ \{ \textnormal{Functors $F: \operatorname{Tw}(\operatorname{\mathcal{A}}) \rightarrow \underline{\operatorname{Hom}}_{\operatorname{\mathcal{C}}}(X,Y)$} \} \ar [d]^{\sim } \\ \{ \textnormal{Morphisms of simplicial sets $\operatorname{N}_{\bullet }(\operatorname{\mathcal{A}}) \rightarrow \operatorname{Hom}_{ \operatorname{N}_{\bullet }^{\operatorname{D}}(\operatorname{\mathcal{C}})}(X,Y)$} \} . } \]