{"paper":{"title":"Balanced systems for $\\mathrm{Hom}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Marco A. P\\'erez, Octavio Mendoza, V\\'ictor Becerril","submitted_at":"2022-03-23T02:16:16Z","abstract_excerpt":"From the notion of (co)generator in relative homological algebra, we present the concept of finite balanced system $[(\\mathcal{X} , \\omega ); (\\nu, \\mathcal{Y})]$ as a tool to induce balanced pairs $(\\mathcal{X} , \\mathcal{Y} )$ for the $\\mathrm{Hom}$ functor with domain determined by the finiteness of homological dimensions relative to $\\mathcal{X}$ and $\\mathcal{Y}$.\n  This approach to balance will cover several well known ambients where right derived functors of $\\mathrm{Hom}$ are obtained relative to certain classes of objects in an abelian category, such as Gorenstein projective and injec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.12140","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/2203.12140/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"}