Theorem 5.2.7.1 (The Fundamental Theorem of Covering Space Theory). Let $S$ be a topological space which is semilocally simply connected. Then the construction $X \mapsto \operatorname{hTr}_{X/S}$ determines an equivalence of categories
\[ \{ \textnormal{Covering maps $f: X \rightarrow S$} \} \rightarrow \operatorname{Fun}( \pi _{\leq 1}(S), \operatorname{Set}). \]