A Grothendieck-Witt space for stable infinity categories with duality

2016/10/31 by Spitzweck, Markus
#19G38 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1610.10044

Abstract

We construct a Grothendieck-Witt space for any stable infinity category with duality. If we apply our construction to perfect complexes over a commutative ring in which 2 is invertible we recover the classical Grothendieck-Witt space. Our Grothendieck-Witt space is a grouplike E-infinity space which is part of a genuine C₂-spectrum, the connective real K-theory spectrum.

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