Inverting endomorphism categories produces a stable homotopy theory of higher categories in which categorical spectra classify homology theories via a categorical Brown representability theorem.
A categorified Dold-Kan correspondence.Selecta Mathematica, 27(2):14
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Stable homotopy theory of higher categories
Inverting endomorphism categories produces a stable homotopy theory of higher categories in which categorical spectra classify homology theories via a categorical Brown representability theorem.