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2017 Stable Postnikov data of Picard $2$–categories
Nick Gurski, Niles Johnson, Angélica Osorno, Marc Stephan
Algebr. Geom. Topol. 17(5): 2763-2806 (2017). DOI: 10.2140/agt.2017.17.2763

Abstract

Picard 2–categories are symmetric monoidal 2–categories with invertible 0–, 1– and 2–cells. The classifying space of a Picard 2–category D is an infinite loop space, the zeroth space of the K–theory spectrum KD. This spectrum has stable homotopy groups concentrated in levels 0, 1 and 2. We describe part of the Postnikov data of KD in terms of categorical structure. We use this to show that there is no strict skeletal Picard 2–category whose K–theory realizes the 2–truncation of the sphere spectrum. As part of the proof, we construct a categorical suspension, producing a Picard 2–category ΣC from a Picard 1–category C, and show that it commutes with K–theory, in that KΣC is stably equivalent to ΣKC.

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Nick Gurski. Niles Johnson. Angélica Osorno. Marc Stephan. "Stable Postnikov data of Picard $2$–categories." Algebr. Geom. Topol. 17 (5) 2763 - 2806, 2017. https://doi.org/10.2140/agt.2017.17.2763

Information

Received: 8 July 2016; Revised: 1 March 2017; Accepted: 27 March 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06791383
MathSciNet: MR3704242
Digital Object Identifier: 10.2140/agt.2017.17.2763

Subjects:
Primary: 55S45
Secondary: 18C20, 18D05, 19D23, 55P42

Rights: Copyright © 2017 Mathematical Sciences Publishers

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