{"paper":{"title":"Special precovers and preenvelopes of complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.KT","authors_text":"Zhanping Wang, Zhongkui Liu","submitted_at":"2013-01-28T16:34:05Z","abstract_excerpt":"The notion of an $\\mathcal{L}$ complex (for a given class of $R$-modules $\\mathcal{L}$) was introduced by Gillespie: a complex $C$ is called $\\mathcal{L}$ complex if $C$ is exact and $\\Z_{i}(C)$ is in $\\mathcal{L}$ for all $i\\in \\mathbb{Z}$. Let $\\widetilde{\\mathcal{L}}$ stand for the class of all $\\mathcal{L}$ complexes. In this paper, we give sufficient condition on a class of $R$-modules such that every complex has a special $\\widetilde{\\mathcal{L}}$-precover (resp., $\\widetilde{\\mathcal{L}}$-preenvelope). As applications, we obtain that every complex has a special projective precover and a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6595","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"}