{"paper":{"title":"A Quillen model structure on the category of Kontsevich-Soibelman weakly unital dg categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.KT","authors_text":"Boris Shoikhet, Piergiorgio Panero","submitted_at":"2019-07-18T10:29:10Z","abstract_excerpt":"In this paper, we study weakly unital dg categories as they were defined by Kontsevich and Soibelman [KS, Sect.4]. We construct a cofibrantly generated Quillen model structure on the category $\\mathrm{Cat}_{\\mathrm{dgwu}}(\\Bbbk)$ of small weakly unital dg categories over a field $\\Bbbk$. Our model structure can be thought of as an extension of the model structure on the category $\\mathrm{Cat}_{\\mathrm{dg}}(\\Bbbk)$ of (strictly unital) small dg categories over $\\Bbbk$, due to Tabuada [Tab]. More precisely, we show that the imbedding of $\\mathrm{Cat}_{\\mathrm{dg}}(\\Bbbk)$ to $\\mathrm{Cat}_{\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07970","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"}