Kerodon

$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Question 1.0.0.1. Let $X$ be a topological space. Can one devise a “category-theoretic” invariant of $X$, in the spirit of the fundamental groupoid $\pi _{\leq 1}(X)$, which contains information about all the homotopy groups of $X$?