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