{"paper":{"title":"Categorical spectra as pointed $(\\infty,\\mathbb{Z})$-categories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"David Kern","submitted_at":"2024-10-03T15:24:30Z","abstract_excerpt":"Lessard's $\\mathbb{Z}$-categories are an analogue of $\\omega$-categories possessing cells in all positive and negative dimensions. Categorical spectra, developed by Stefanich, are an analogue of spectra obtained by replacing the suspension of pointed $\\infty$-groupoids by that of pointed $(\\infty,\\omega)$-categories. We give an $\\infty$-categorical definition of weak $\\mathbb{Z}$-categories (alias $(\\infty,\\mathbb{Z})$-categories), and show categorical spectra to be equivalent to pointed $(\\infty,\\mathbb{Z})$-categories. In particular, we show that the stable cells of categorical spectra coinc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.02578","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.02578/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}