{"paper":{"title":"Comparing $\\mathrm{Add}(M)$ with $\\mathrm{Prod}(M)$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Cristian Rafiliu, Simion Breaz","submitted_at":"2025-01-15T18:17:29Z","abstract_excerpt":"We present characterizations for the inclusions $\\mathrm{Add}(M)\\subseteq \\mathrm{Prod}(M)$ and $\\mathrm{Prod}(M)\\subseteq \\mathrm{Add}(M)$ in locally finitely presented categories and in compactly generated triangulated categories. As applications, we describe the situations when the classes of the form $\\mathrm{Prod}(M)$ and $\\mathrm{Add}(M)$ are (pre)covering, respectively (pre)enveloping."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.08993","kind":"arxiv","version":2},"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/2501.08993/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"}