English

Infinity categories with duality and hermitian multiplicative infinite loop space machines

K-Theory and Homology 2025-04-01 v4 Algebraic Topology Category Theory

Abstract

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.

Keywords

Cite

@article{arxiv.1610.10043,
  title  = {Infinity categories with duality and hermitian multiplicative infinite loop space machines},
  author = {Hadrian Heine and Alejo Lopez-Avila and Markus Spitzweck},
  journal= {arXiv preprint arXiv:1610.10043},
  year   = {2025}
}

Comments

26 pages

R2 v1 2026-06-22T16:37:51.498Z