{"paper":{"title":"Generalized equivariant model structures on $\\mathbf{Cat}^I$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Yuzhou Gu","submitted_at":"2016-05-25T17:50:18Z","abstract_excerpt":"Let $I$ be a small category, $\\mathcal{C}$ be the category $\\mathbf{Cat}$, $\\mathbf{Ac}$ or $\\mathbf{Pos}$ of small categories, acyclic categories, or posets, respectively. Let $\\mathcal{O}$ be a locally small class of objects in $\\mathbf{Set}^I$ such that $\\mathrm{colim}_I O=*$ for every $O\\in \\mathcal{O}$. We prove that $\\mathcal{C}^I$ admits the $\\mathcal{O}$-equivariant model structure in the sense of Farjoun, and that it is Quillen equivalent to the $\\mathcal{O}$-equivariant model structure on $\\mathbf{sSet}^I$. This generalizes previous results of Bohmann-Mazur-Osorno-Ozornova-Ponto-Yarn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07983","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"}