Infinity categories with duality and hermitian multiplicative infinite loop space machines

We show that any preadditive infinity category with duality gives rise to a direct sum hermitian K-theory spectrum. This assignment is lax symmetric monoidal, thereby producing E-infinity ring spectra from preadditive symmetric monoidal infinity categories with duality. To have examples of preadditi...

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Bibliographic Details
Published in:arXiv.org 2024-03
Main Authors: Heine, Hadrian, Lopez-Avila, Alejo, Spitzweck, Markus
Format: Article
Language:English
Subjects:
Infinity
Rings (mathematics)
Online Access:Get full text
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Summary:We show that any preadditive infinity category with duality gives rise to a direct sum hermitian K-theory spectrum. This assignment is lax symmetric monoidal, thereby producing E-infinity ring spectra from preadditive symmetric monoidal infinity categories with duality. To have examples of preadditive symmetric monoidal infinity categories with duality we show that any preadditive symmetric monoidal infinity category, in which every object admits a dual, carries a canonical duality. Moreover we classify and twist the dualities in various ways and apply our definitions for example to finitely generated projective modules over E-infinity ring spectra.
ISSN:2331-8422