{"paper":{"title":"Magmal characterisations of cocartesian categories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Nathanael Arkor","submitted_at":"2025-08-15T17:28:48Z","abstract_excerpt":"We present a survey of characterisations of cocartesian categories in terms of monoidal categories - and, more generally, magmal categories - satisfying additional properties. In particular, we show that the following are equivalent for a unital magmal category $(\\mathcal M, \\otimes)$, sharpening several classical characterisations.\n  * $(\\mathcal M, \\otimes)$ is cocartesian monoidal.\n  * Every object of $\\mathcal M$ admits the structure of a unital magma with respect to $\\otimes$, such that every morphism is a homomorphism, and a single compatibility condition holds between the magma structur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.11615","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.11615/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"}