{"paper":{"title":"A semi-model structure for Grothendieck weak 3-groupoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Edoardo Lanari","submitted_at":"2018-09-21T02:55:16Z","abstract_excerpt":"In this paper we apply some tools developed in our previous work on Grothendieck $\\infty$-groupoids to the finite-dimensional case of weak 3-groupoids.\n  We obtain a semi-model structure on the category of Grothendieck 3-groupoids of suitable type, thanks to the construction of an endofunctor $\\mathbb{P}$ that has enough structure to behave like a path object. This makes use of a recognition principle we prove here that characterizes globular theories whose models can be viewed as Grothendieck $n$-groupoids (for $0\\leq n \\leq \\infty$). Finally, we prove that the obstruction in arbitrary dimens"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07923","kind":"arxiv","version":1},"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"}