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We propose a new definition of Kuranishi space, which has the nice property that they form a 2-category $\\bf Kur$. Thus the homotopy category Ho$({\\bf Kur})$ is an ordinary category of Kuranishi spaces.\n  Any Fukaya-Oh-Ohta-Ono (FOOO) Kuranishi space $\\bf X$ can be made into a compact Kuranishi space $\\bf X'$ uniquely up to"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1510.07444","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-10-26T11:49:47Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"6bdb1effaeab4199a6ab329272ee10d0244403d40abb1102ae0347c6ca3ad757","abstract_canon_sha256":"7b13aa55e29a69884698f46dcbe48956bbecf2bf70b94773a806ae0a3eac4b7e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:56.770577Z","signature_b64":"7IkmRlFP64+tVq1XK/K0MOD5cdLV2N9ZR14CeYKGh8ovKtjFiF3MWyRfIJjjesgP6y7SqaxevTlrR4sdGU3LAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9afe3ec9252420936b10368ad64029ef233ec3f4ec9a5ad31dde444ceb55b237","last_reissued_at":"2026-05-18T00:06:56.769990Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:56.769990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kuranishi spaces as a 2-category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Dominic Joyce","submitted_at":"2015-10-26T11:49:47Z","abstract_excerpt":"This is a survey of the author's paper arXiv:1409.6908 and in-progress book. 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