{"paper":{"title":"Generalized covering space theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.GN"],"primary_cat":"math.AT","authors_text":"Jeremy Brazas","submitted_at":"2015-08-20T15:17:20Z","abstract_excerpt":"In this paper, we unify various approaches to generalized covering space theory by introducing a categorical framework in which coverings are defined purely in terms of unique lifting properties. For each category $\\mathcal{C}$ of path-connected spaces having the unit disk as an object, we construct a category of $\\mathcal{C}$-coverings over a given space $X$ that embeds in the category of $\\pi_1(X,x_0)$-sets via the usual monodromy action on fibers. When $\\mathcal{C}$ is extended to its coreflective hull $\\mathscr{H}(\\mathcal{C})$, the resulting category of based $\\mathscr{H}(\\mathcal{C})$-co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05004","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"}