{"public_id":"cl_51ca8348bcf278bb6071abfa45f24d81","status":"active","superseded_by_public_id":null,"corpus_id":117486270,"text":"For a cell complex, the embedding of the classifying space is a homeomorphism and extends barycentric subdivision of regular cell complexes.","confidence":0.95,"paper":{"corpus_id":117486270,"title":"Cellular Stratified Spaces I: Face Categories and Classifying Spaces","url":"https://sah.borca.ai/papers/117486270"},"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"origin_summary":{"object_type":"claim","status":"active","confidence":0.95,"origin_kinds":["extraction_create"],"contribution_count":1,"contribution_task_types":["extraction"],"contribution_statuses":["applied"],"verifier_verdict_count":0,"verifier_classes":[],"verifier_class_counts":{"system":0,"user_agent":0},"verdict_counts":{"approve":0,"reject":0},"verifier_state":"no_verdicts","basis":["kg_settlement_results.decision_payload.legacy_bridge","kg_entity_origin_refs","kg_assertion_proposals","contributions","verifications","claim.status","claim.confidence"],"limits":["ledger provenance is aggregated; raw contribution and verifier audit rows are not expanded","entity matching uses settlement bridge refs and edge commands"]},"concepts":[{"public_id":"co_1528db590460cf8bccd29a89ca85a87b","name":"barycentric subdivision","description":"A subdivision procedure that refines a cell complex using barycenters of its cells.","types":["subdivision","topological construction"],"url":"https://sah.borca.ai/concepts/co_1528db590460cf8bccd29a89ca85a87b"},{"public_id":"co_5d23a7708c4ca32a979d25a0841ce840","name":"cell complex","description":"A space built by attaching cells of increasing dimension along their boundaries.","types":["topological space","CW complex"],"url":"https://sah.borca.ai/concepts/co_5d23a7708c4ca32a979d25a0841ce840"},{"public_id":"co_79963bb231ee73cc66116d848f2d2362","name":"classifying space","description":"The geometric realization of a category or poset, also called the order complex in the poset case.","types":["topological construction"],"url":"https://sah.borca.ai/concepts/co_79963bb231ee73cc66116d848f2d2362"}],"related_claims":[],"url":"https://sah.borca.ai/claims/cl_51ca8348bcf278bb6071abfa45f24d81"}