Kerodon

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

Corollary 5.6.1.10. Let $\operatorname{\mathcal{C}}$ be a Kan complex. Then the construction $(U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}) \mapsto \operatorname{hTr}_{\operatorname{\mathcal{E}}/\operatorname{\mathcal{C}}}$ induces an equivalence of categories

\[ \{ \textnormal{Covering maps $\operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$} \} \rightarrow \operatorname{Fun}( \pi _{\leq 1}(\operatorname{\mathcal{C}}), \operatorname{Set}). \]