{"paper":{"title":"Combinatorial categorical equivalences of Dold-Kan type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Ross Street, Stephen Lack","submitted_at":"2014-02-28T07:15:36Z","abstract_excerpt":"We prove a class of equivalences of additive functor categories that are relevant to enumerative combinatorics, representation theory, and homotopy theory. Let $\\mathscr{X}$ denote an additive category with finite direct sums and split idempotents. The class includes (a) the Dold-Puppe-Kan theorem that simplicial objects in $\\mathscr{X}$ are equivalent to chain complexes in $\\mathscr{X}$; (b) the observation of Church, Ellenberg and Farb that $\\mathscr{X}$-valued species are equivalent to $\\mathscr{X}$-valued functors from the category of finite sets and injective partial functions; (c) a resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.7151","kind":"arxiv","version":5},"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"}