{"paper":{"title":"Phantom covering ideals in categories without enough projective morphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CT"],"primary_cat":"math.KT","authors_text":"Pedro A. Guil Asensio, Sergio Estrada, Sinem Odabasi","submitted_at":"2016-07-21T23:35:42Z","abstract_excerpt":"We give sufficient conditions to ensure that the ideal $\\Phi(\\mathcal E)$ of $\\mathcal E$-phantom maps in a locally $\\lambda$-presentable exact category $(\\mathcal{A}, \\mathcal{E})$ is (special) (pre)covering ideal, where $\\mathcal E$ is an exact substructure of $(\\mathcal{A}, \\mathcal{E})$. As a byproduct, we infer the existence of various covering ideals in categories of sheaves which have a meaningful geometrical motivation. In particular we deal with a Zariski-local notion of phantom maps in categories of sheaves. We would like to point out that our approach is necessarily different from ["},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06529","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":""},"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"}