{"paper":{"title":"Graded Leinster monoids and generalized Deligne conjecture for 1-monoidal abelian categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.QA","authors_text":"Boris Shoikhet","submitted_at":"2015-04-10T05:19:13Z","abstract_excerpt":"In our recent paper [Sh1] a version of the \"generalized Deligne conjecture\" for abelian $n$-fold monoidal categories is proven. For $n=1$ this result says that, given an abelian monoidal $k$-linear category $\\mathscr{A}$ with unit $e$, $k$ a field of characteristic 0, the dg vector space $\\mathrm{RHom}_{\\mathscr{A}}(e,e)$ is the first component of a Leinster 1-monoid in $\\mathscr{A}lg(k)$ (provided a rather mild condition on the monoidal and the abelian structures in $\\mathscr{A}$, called homotopy compatibility, is fulfilled).\n  In the present paper, we introduce a new concept of a ${\\it grade"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02552","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"}