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We prove that $F$ is canonically isomorphic to the right derived DG functor $RH^0(F)$. We also prove a similar result for bounded derived DG categories in a more general setting. We give an example showing that the corresponding statements for triangulated fu"},"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":"1004.1918","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2010-04-12T10:30:29Z","cross_cats_sorted":[],"title_canon_sha256":"c1814a43d98be9741327d762c7260fbdd3e0a4d55fb3eac1196b707bcbe2fa19","abstract_canon_sha256":"9f0f2a534ba7e30824df048730a0f29be31c823e88f4cbfdbd8e256bd2d38b39"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:01.763476Z","signature_b64":"v6GsoPXSo/v9iHcFg+tJjWvByVuZOhbupnsPCPvD1V2ql5Nu7koY+okZnLlUjbPY+d9M1bhb5fqn7Ft4Dc+6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"647fb5c400928b92d1c1f8b1f885d6e1d84c5b4df83c172cc3cff4360a894d30","last_reissued_at":"2026-05-18T04:32:01.763003Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:01.763003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the derived DG functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Vadim Vologodsky","submitted_at":"2010-04-12T10:30:29Z","abstract_excerpt":"Assume that abelian categories $A, B$ over a field admit countable direct limits and that these limits are exact. Let $F: D^+_{dg}(A) --> D^+_{dg}(B)$ be a DG quasi-functor such that the functor $Ho(F): D^+(A) \\to D^+(B)$ carries $D^{\\geq 0}(A)$ to $D^{\\geq 0}(B)$ and such that, for every $i>0$, the functor $H^i F: A \\to B$ is effaceable. We prove that $F$ is canonically isomorphic to the right derived DG functor $RH^0(F)$. We also prove a similar result for bounded derived DG categories in a more general setting. 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