{"paper":{"title":"Multiplicativity of Connes' calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Partha Sarathi Chakraborty, Satyajit Guin","submitted_at":"2014-02-24T07:18:16Z","abstract_excerpt":"We consider the quadruples $\\,(\\mathcal{A},\\mathbb{V},D,\\gamma)$ where $\\mathcal{A}$ is a unital, associative $\\mathbb{K}\\,$-algebra represented on the $\\mathbb{K}\\,$-vector space $\\mathbb{V}$, $D\\in \\mathcal{E}nd(\\mathbb{V})$, $\\gamma\\in\\mathcal{E}nd(\\mathbb{V})$ is a $\\mathbb{Z}_2$-grading operator which commutes with $\\mathcal{A}$ and anticommutes with $D$. We prove that the collection of such quadruples, denoted by $\\,\\widetilde{\\mathcal{S}pec}\\,$, is a monoidal category. We consider the monoidal subcategory $\\,\\widetilde{\\mathcal{S}pec_{sub}}\\,$ of objects of $\\,\\widetilde{\\mathcal{S}pec}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5735","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"}