{"paper":{"title":"Pretorsion theories in general categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.RA"],"primary_cat":"math.CT","authors_text":"Alberto Facchini, Carmelo Finocchiaro, Marino Gran","submitted_at":"2019-08-09T17:16:53Z","abstract_excerpt":"We present a setting for the study of torsion theories in general categories. The idea is to associate, with any pair ($\\mathcal T$, $\\mathcal F$) of full replete subcategories in a category $\\mathcal C$, the corresponding full subcategory $\\mathcal Z = \\mathcal T \\cap \\mathcal F$ of \\emph{trivial objects} in $\\mathcal C$. The morphisms which factor through $\\mathcal Z$ are called $\\mathcal Z$-trivial, and these form an ideal of morphisms, with respect to which one can define $\\mathcal Z$-prekernels, $\\mathcal Z$-precokernels, and short $\\mathcal Z$-preexact sequences. This naturally leads to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03546","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/1908.03546/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"}