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Stable homotopy theory is that part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor.
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"Characteristics" (thick subcategories) in $n$-groupoids
$
\newcommand{\Ab}{\mathbf{Ab}}
\newcommand{\Sp}{\mathbf{Sp}}
$In 0-groupoids (sets), the thick subcategories of the category of abelian groups $\Ab$ are given by the primes $p$ and $0$, which we can …
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What's the stabilization of the $\infty$-category of $\infty$-categories?
$\require{AMScd}$One nice thing about $\infty$-categories is that spaces are themselves $\infty$-categories. What's the analogue for spectra? Presumably this would be the stabilization of the $\infty$ …