Gurski, N., Johnson, N., Osorno, A.M. et al. (1 more author) Stable Postnikov data of Picard 2-categories. (Unpublished)
Abstract
Picard 2-categories are symmetric monoidal 2-categories with invertible 0-, 1-, and 2-cells. The classifying space of a Picard 2-category $\mathcal{D}$ is an infinite loop space, the zeroth space of the $K$-theory spectrum $K\mathcal{D}$. This spectrum has stable homotopy groups concentrated in levels 0, 1, and 2. In this paper, we describe part of the Postnikov data of $K\mathcal{D}$ 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 $\Sigma C$ from a Picard 1-category $C$, and show that it commutes with $K$-theory in that $K\Sigma C$ is stably equivalent to $\Sigma K C$.
Metadata
Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 The Author(s). Please contact the authors for reuse permissions | ||||
Keywords: | math.AT; math.AT; math.CT; math.KT; Primary: 55S45, Secondary: 18C20, 55P42, 19D23, 18D05 | ||||
Institution: | The University of Sheffield | ||||
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) | ||||
Funding Information: |
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Depositing User: | Symplectic Sheffield | ||||
Date Deposited: | 15 Mar 2017 13:30 | ||||
Last Modified: | 15 Mar 2017 13:30 | ||||
Status: | Unpublished | ||||
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