Kerodon

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

Question 11.5.0.14. Given a topological space $X$, what can we say about the collection of sets $\{ \operatorname{Sing}_{n}(X) \} _{n \geq 0}$, together with the face and degeneracy operators

\[ d^{n}_{i}: \operatorname{Sing}_{n}(X) \rightarrow \operatorname{Sing}_{n-1}(X) \quad \quad s^{n}_ i: \operatorname{Sing}_{n}(X) \rightarrow \operatorname{Sing}_{n+1}(X)? \]

What sort of mathematical structure do they form?