Kerodon

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Question 1.1.0.3. 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 maps

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

What sort of mathematical structure do they form?