{"paper":{"title":"Comparing cohomology obstructions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"David Blanc, Hans-Joachim Baues","submitted_at":"2010-08-10T13:30:26Z","abstract_excerpt":"We show that three different kinds of cohomology - Baues-Wirsching cohomology, the (S,O)-cohomology of Dwyer-Kan, and the Andre-Quillen cohomology of a Pi-algebra - are isomorphic, under certain assumptions.\n  This is then used to identify the cohomological obstructions in three general approaches to realizability problems: the track category version of Baues-Wirsching, the diagram rectifications of Dwyer-Kan-Smith, and the Pi-Algebra realization of Dwyer-Kan-Stover. Our main tool in this identification is the notion of a mapping algebra: a simplicially enriched version of an algebra over a th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1712","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"}