{"paper":{"title":"Classical Distributive Restriction Categories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.CT","authors_text":"Jean-Simon Pacaud Lemay, Robin Cockett","submitted_at":"2023-05-25T22:59:47Z","abstract_excerpt":"In the category of sets and partial functions, $\\mathsf{PAR}$, while the disjoint union $\\sqcup$ is the usual categorical coproduct, the Cartesian product $\\times$ becomes a restriction categorical analogue of the categorical product: a restriction product. Nevertheless, $\\mathsf{PAR}$ does have a usual categorical product as well in the form $A \\& B := A \\sqcup B \\sqcup (A \\times B)$. Surprisingly, asking that a distributive restriction category (a restriction category with restriction products $\\times$ and coproducts $\\oplus$) has $A \\& B$ a categorical product is enough to imply that the ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.16524","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.16524/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}