Hadrian Heine, Alejo Lopez-Avila, Markus Spitzweck
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Infinity categories with duality and hermitian multiplicative infinite loop space machines
We show that any preadditive ∞-category with duality gives rise to a direct sum hermitian K-theory spectrum. This assignment is lax symmetric monoidal, thereby producing -ring spectra from preadditive symmetric monoidal ∞-categories with duality. To have examples of preadditive symmetric monoidal ∞-categories with duality we show that any preadditive symmetric monoidal ∞-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 -ring spectra.
期刊介绍:
The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.