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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1605.07983","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-05-25T17:50:18Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"005bea11e42185332d1c9b2ef9de5d86a3fcdf76f32feba9e440a11fb5cf1a1d","abstract_canon_sha256":"824a82d4f08a55da92b2f03b486f18795d1731fcf13985da7e8c0b4d14c7a26d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:38.647232Z","signature_b64":"9ERMQKV1NMo/AIi+fQULQagIcy+hd1v8PTiqPyx0//xzZ/8i4rt4VCsBMgb134kQxBn09PunBCHPxFI2W02MBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c0de57e284b3a0f92c0b75832fcedbda2a447a0973db6344cbac73b10b3815d","last_reissued_at":"2026-05-18T01:13:38.646600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:38.646600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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