{"paper":{"title":"Conditionally flat functors on spaces and groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Emmanuel Dror Farjoun, Jerome Scherer","submitted_at":"2013-09-03T14:11:23Z","abstract_excerpt":"Consider an extension of groups 1 -> K -> G -> Q -> 1 which enjoys the property that the quotient by the lower central series Gamma_{c+1} produces another extension 1 -> K/ Gamma_{c+1} K -> G /Gamma_{c+1} G -> Q / Gamma_{c+1} Q -> 1, of nilpotent groups of class c. We say that the extension is Gamma_{c+1}-flat. Let us pull back the original extension along any homomorphism X -> Q. Does the pullback extension enjoy the same Gamma_{c+1}-flatness property?\n  To answer this question we consider not only quotients by the lower central series, but any localization functor in the category of groups. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0686","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"}