Remark 1.5.1.8. Let $X$ be a topological space and let $\operatorname{\mathcal{C}}$ be an arbitrary $\infty $-category. Motivated by Example 1.5.1.7, one can define a $\operatorname{\mathcal{C}}$-valued local system on $X$ to be a functor of $\infty $-categories $\operatorname{Sing}_{\bullet }(X) \rightarrow \operatorname{\mathcal{C}}$. Beware that this notion generally cannot be reformulated in terms of the fundamental groupoid $\pi _{\leq 1}(X)$.
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