Ambidexterity and height

Shachar Carmeli, Tomer M. Schlank, Lior Yanovski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We introduce and study the notion of semiadditive height for higher semiadditive ∞-categories, which generalizes the chromatic height. We show that the higher semiadditive structure trivializes above the height and prove a form of the redshift principle, in which categorification increases the height by one. In the stable setting, we show that a higher semiadditive ∞-category decomposes into a product according to height, and relate the notion of height to semisimplicity properties of local systems. We place the study of higher semiadditivity and stability in the general framework of smashing localizations of PrL, which we call modes. Using this theory, we introduce and study the universal stable ∞-semiadditive ∞-category of semiadditive height n, and give sufficient conditions for a stable 1-semiadditive ∞-category to be ∞-semiadditive.

Original languageAmerican English
Article number107763
JournalAdvances in Mathematics
Volume385
DOIs
StatePublished - 16 Jul 2021

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Inc.

Keywords

  • Ambidexterity
  • Chromatic
  • Mode
  • Semiadditivity

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