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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.

17 votes
1 answer
1k views

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 $\infty$ …
5 votes
0 answers
136 views

"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 …