Kerodon

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

Remark 1.4.1.8. Let $X$ be a topological space and let $\operatorname{\mathcal{C}}$ be an arbitrary $\infty $-category. Motivated by Example 1.4.1.7, 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 $\pi _{\leq 1}(X)$.