nLab
stable infinity-category

A stable $\mathrm{\infty }$-category is an ∞-category whose objects behave like homotopy-theoretic spectra.

A detailed theory for stable $\mathrm{\infty }$-categories exists for the case of (∞,1)-categories: see stable (∞,1)-category.

This type of stability is not to be confused with being stably (or symmetric) monoidal.

References

• Jacob Lurie, Stable ∞-Categories.