{"paper":{"title":"Stable Postnikov data of Picard 2-categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.KT"],"primary_cat":"math.AT","authors_text":"Ang\\'elica M. Osorno, Marc Stephan, Nick Gurski, Niles Johnson","submitted_at":"2016-06-22T18:16:38Z","abstract_excerpt":"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 ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07032","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}