{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:J5BAXLA63QDM7ITKCJLE2KG3KZ","short_pith_number":"pith:J5BAXLA6","schema_version":"1.0","canonical_sha256":"4f420bac1edc06cfa26a12564d28db56727ce3bc4e8edc4301f56a61916cd2cd","source":{"kind":"arxiv","id":"1803.09451","version":2},"attestation_state":"computed","paper":{"title":"Derived categories for Grothendieck categories of enriched functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.CT","authors_text":"Darren Jones, Grigory Garkusha","submitted_at":"2018-03-26T07:47:55Z","abstract_excerpt":"The derived category $D[C,V]$ of the Grothendieck category of enriched functors $[C,V]$, where $V$ is a closed symmetric monoidal Grothendieck category and $C$ is a small $V$-category, is studied. We prove that if the derived category $D(V)$ of $V$ is a compactly generated triangulated category with certain reasonable assumptions on compact generators or $K$-injective resolutions, then the derived category $D[C,V]$ is also compactly generated triangulated. Moreover, an explicit description of these generators is given."},"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":"1803.09451","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-03-26T07:47:55Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"7ebae24bc3d11291f3603b9da9337f9245ce19efbd9184a73ab8dfe95ea5bbdb","abstract_canon_sha256":"e23c44964cf1f447a56c5cc6835a5d693c1a8564d614ce3010b8309cf1494404"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:36.976369Z","signature_b64":"3j/GyeYZlYVv7ONZO9PuUAYtvx46t1NFD+x4UXPhLuoQ5mGsk+AD7g8H/fRebTuH+IXcqgSb1DrXx/Qb2GGZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f420bac1edc06cfa26a12564d28db56727ce3bc4e8edc4301f56a61916cd2cd","last_reissued_at":"2026-05-18T00:03:36.975785Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:36.975785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Derived categories for Grothendieck categories of enriched functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.CT","authors_text":"Darren Jones, Grigory Garkusha","submitted_at":"2018-03-26T07:47:55Z","abstract_excerpt":"The derived category $D[C,V]$ of the Grothendieck category of enriched functors $[C,V]$, where $V$ is a closed symmetric monoidal Grothendieck category and $C$ is a small $V$-category, is studied. We prove that if the derived category $D(V)$ of $V$ is a compactly generated triangulated category with certain reasonable assumptions on compact generators or $K$-injective resolutions, then the derived category $D[C,V]$ is also compactly generated triangulated. Moreover, an explicit description of these generators is given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09451","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1803.09451","created_at":"2026-05-18T00:03:36.975883+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.09451v2","created_at":"2026-05-18T00:03:36.975883+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.09451","created_at":"2026-05-18T00:03:36.975883+00:00"},{"alias_kind":"pith_short_12","alias_value":"J5BAXLA63QDM","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"J5BAXLA63QDM7ITK","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"J5BAXLA6","created_at":"2026-05-18T12:32:31.084164+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J5BAXLA63QDM7ITKCJLE2KG3KZ","json":"https://pith.science/pith/J5BAXLA63QDM7ITKCJLE2KG3KZ.json","graph_json":"https://pith.science/api/pith-number/J5BAXLA63QDM7ITKCJLE2KG3KZ/graph.json","events_json":"https://pith.science/api/pith-number/J5BAXLA63QDM7ITKCJLE2KG3KZ/events.json","paper":"https://pith.science/paper/J5BAXLA6"},"agent_actions":{"view_html":"https://pith.science/pith/J5BAXLA63QDM7ITKCJLE2KG3KZ","download_json":"https://pith.science/pith/J5BAXLA63QDM7ITKCJLE2KG3KZ.json","view_paper":"https://pith.science/paper/J5BAXLA6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.09451&json=true","fetch_graph":"https://pith.science/api/pith-number/J5BAXLA63QDM7ITKCJLE2KG3KZ/graph.json","fetch_events":"https://pith.science/api/pith-number/J5BAXLA63QDM7ITKCJLE2KG3KZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J5BAXLA63QDM7ITKCJLE2KG3KZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J5BAXLA63QDM7ITKCJLE2KG3KZ/action/storage_attestation","attest_author":"https://pith.science/pith/J5BAXLA63QDM7ITKCJLE2KG3KZ/action/author_attestation","sign_citation":"https://pith.science/pith/J5BAXLA63QDM7ITKCJLE2KG3KZ/action/citation_signature","submit_replication":"https://pith.science/pith/J5BAXLA63QDM7ITKCJLE2KG3KZ/action/replication_record"}},"created_at":"2026-05-18T00:03:36.975883+00:00","updated_at":"2026-05-18T00:03:36.975883+00:00"}