{"paper":{"title":"Von Neumann Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Marc Comeau, Richard Blute","submitted_at":"2012-09-01T19:13:55Z","abstract_excerpt":"In this paper, we introduce the notion of a von Neumann category, as a generalization and categorification of von Neumann algebra. A von Neumann category is a premonoidal category with compatible dagger structure which embeds as a double commutant into a suitable premonoidal category of Hilbert spaces.\n  The notion was inspired by algebraic quantum field theory. In AQFT, one assigns to open regions in Minkowski space a C*-algebra, called the local algebra. The local algebras are patched together to form a global algebra associated to the AQFT. The key relativistic assumption is Einstein Causal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0124","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"}