{"paper":{"title":"Approximations and Mittag-Leffler conditions --- the applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jan Trlifaj, Jan \\v{S}aroch, Lidia Angeleri H\\\"ugel","submitted_at":"2016-12-04T16:44:44Z","abstract_excerpt":"A classic result by Bass says that the class of all projective modules is covering, if and only if it is closed under direct limits. Enochs extended the if-part by showing that every class of modules $\\mathcal C$, which is precovering and closed under direct limits, is covering, and asked whether the converse is true. We employ the tools developed in [18] and give a positive answer when $\\mathcal C = \\mathcal A$, or $\\mathcal C$ is the class of all locally $\\mathcal A ^{\\leq \\omega}$-free modules, where $\\mathcal A$ is any class of modules fitting in a cotorsion pair $(\\mathcal A, \\mathcal B)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01140","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":""},"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"}