Wiki. “球谱” [球谱]

If you (like many people working in homotopy theory and/or higher category theory and/or homotopy type theory) think that spaces are the real fundamental objects and sets are just the reflective subcategories of $0$-truncated space, then the role usually played by $\mathbb{Z}$ in traditional set-based mathematics is now played by $\mathbb S$, and $\mathbb Z$ only appear as the $0$-truncation of $\mathbb S$.

有限集合与双射的范畴的几何实现具有同伦型 $\coprod_{n\geq 0}B\Sigma_n$. 关于加法完备化为群, 得到的同伦型是 $\operatorname{colim}_{k\to\infty}\Omega^k S^k \simeq \Omega^\infty \mathbb S$.