2016/10/31 by Hadrian Heine, Heine, Hadrian, Alejo Lopez-Avila +3 · 1 voice
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AT #math.CT #math.KT
paper · pdf · doi:10.48550/arxiv.1610.10043
arxiv published 2016/10/31 · arxiv updated 2025/03/31
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.