{"paper":{"title":"Minimality in diagrams of simplicial sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Carles Broto, Carlos Giraldo, Ram\\'on Flores","submitted_at":"2018-04-17T16:27:10Z","abstract_excerpt":"We formulate the concept of minimal fibration in the context of fibrations in the model category $\\mathbf{S}^\\mathcal{C}$ of $\\mathcal{C}$-diagrams of simplicial sets, for a small index category $\\mathcal{C}$. When $\\mathcal{C}$ is an $EI$-category satisfying some mild finiteness restrictions, we show that every fibration of $\\mathcal{C}$-diagrams admits a well-behaved minimal model. As a consequence, we establish a classification theorem for fibrations in $\\mathbf{S}^\\mathcal{C}$ over a constant diagram, generalizing the classification theorem of Barratt, Gugenheim, and Moore for simplicial f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06354","kind":"arxiv","version":4},"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"}