{"paper":{"title":"Cubical $(\\omega,p)$-categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Maxime Lucas","submitted_at":"2016-12-21T10:44:49Z","abstract_excerpt":"In this article we introduce the notion of cubical $(\\omega,p)$-categories, for $p \\in \\mathbb N \\cup \\{\\omega\\}$. We show that the equivalence between globular and groupoid $\\omega$-categories proven by Al-Agl, Brown and Steiner induces an equivalence between globular and cubical $(\\omega,p)$-categories for all $p \\geq 0$. In particular we recover in a more explicit fashion the equivalence between globular and cubical groupoids proven by Brown and Higgins.\n  We also define the notion of $(\\omega,p)$-augmented directed complexes, and show that Steiner's adjunction between augmented directed co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07050","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"}