{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:66FF5DE26RQGKE7VUUOOVHUV2E","short_pith_number":"pith:66FF5DE2","canonical_record":{"source":{"id":"1209.4307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-19T16:54:44Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"30e1f5ca7f2a29dafe9aa3a196bdb4777841751e05d0548b213d3f5e145237f8","abstract_canon_sha256":"241680d391e997a04c0178d5f35defc9917d7fe4a76fde4cb220ee71036273d7"},"schema_version":"1.0"},"canonical_sha256":"f78a5e8c9af4606513f5a51cea9e95d1009cb225164bf1e98272f851785c3bb3","source":{"kind":"arxiv","id":"1209.4307","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4307","created_at":"2026-05-18T03:45:12Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4307v1","created_at":"2026-05-18T03:45:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4307","created_at":"2026-05-18T03:45:12Z"},{"alias_kind":"pith_short_12","alias_value":"66FF5DE26RQG","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"66FF5DE26RQGKE7V","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"66FF5DE2","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:66FF5DE26RQGKE7VUUOOVHUV2E","target":"record","payload":{"canonical_record":{"source":{"id":"1209.4307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-19T16:54:44Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"30e1f5ca7f2a29dafe9aa3a196bdb4777841751e05d0548b213d3f5e145237f8","abstract_canon_sha256":"241680d391e997a04c0178d5f35defc9917d7fe4a76fde4cb220ee71036273d7"},"schema_version":"1.0"},"canonical_sha256":"f78a5e8c9af4606513f5a51cea9e95d1009cb225164bf1e98272f851785c3bb3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:12.925816Z","signature_b64":"jXR3WNcGODOhMOW4+hKq5cMf8U1vnn0CGPXMsCChOi7Mb7m4PudZlYWmWTVdQ6/G/jCGMJXoMANE21GcjfWPAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f78a5e8c9af4606513f5a51cea9e95d1009cb225164bf1e98272f851785c3bb3","last_reissued_at":"2026-05-18T03:45:12.925089Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:12.925089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.4307","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:45:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C65X+MaBYGcAdvUZTWVcBIlYRawIqM9OPwVJ5mVGFYSthsxKy15pUvduoEIPcFU+lnWKmdQK2KfsOptRnmKZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:48:32.541678Z"},"content_sha256":"4c0662516335ebe44138097f81e9b82b06c477065e01f14a17d1422d4dbce090","schema_version":"1.0","event_id":"sha256:4c0662516335ebe44138097f81e9b82b06c477065e01f14a17d1422d4dbce090"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:66FF5DE26RQGKE7VUUOOVHUV2E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derived categories of functors and Fourier--Mukai transform for quiver sheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AG","authors_text":"Marcos Jardim, Paula Olga Gneri","submitted_at":"2012-09-19T16:54:44Z","abstract_excerpt":"Let C be small category and A an arbitrary category. Consider the category C(A) whose objects are functors from C to A, and whose morphisms are natural transformations. Given a functor F : A --> B one obtains an induced functor F_C : C(A) --> C(B) . If A and B are abelian categories, we have that C(A) and C(B) are also abelian, and one has two functors R(F_C) : D(C(A)) --> D(C(B)) and (RF)_ C : C(D(A)) --> C(D (B)). The goals of this paper are: 1) to find a relationship between D (C(A)) and C(D(A)); 2) to relate the functors R(F_C) and (RF)_C. As an application, we prove a version of Mukai's T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4307","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:45:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NzVSTXAiNcEsxYXKWeQmFLP2aJa3Wjlfz5Nxmy1YIiaY1+r52lN3sFPWjabWj274GMMK7P5m8Lg46N+QyyYHDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:48:32.542339Z"},"content_sha256":"25136def4ee400c0c47d574f1c1f5c2a4684c05aede31b8a9a7ed85a4ffa37b2","schema_version":"1.0","event_id":"sha256:25136def4ee400c0c47d574f1c1f5c2a4684c05aede31b8a9a7ed85a4ffa37b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/66FF5DE26RQGKE7VUUOOVHUV2E/bundle.json","state_url":"https://pith.science/pith/66FF5DE26RQGKE7VUUOOVHUV2E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/66FF5DE26RQGKE7VUUOOVHUV2E/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T22:48:32Z","links":{"resolver":"https://pith.science/pith/66FF5DE26RQGKE7VUUOOVHUV2E","bundle":"https://pith.science/pith/66FF5DE26RQGKE7VUUOOVHUV2E/bundle.json","state":"https://pith.science/pith/66FF5DE26RQGKE7VUUOOVHUV2E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/66FF5DE26RQGKE7VUUOOVHUV2E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:66FF5DE26RQGKE7VUUOOVHUV2E","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"241680d391e997a04c0178d5f35defc9917d7fe4a76fde4cb220ee71036273d7","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-19T16:54:44Z","title_canon_sha256":"30e1f5ca7f2a29dafe9aa3a196bdb4777841751e05d0548b213d3f5e145237f8"},"schema_version":"1.0","source":{"id":"1209.4307","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4307","created_at":"2026-05-18T03:45:12Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4307v1","created_at":"2026-05-18T03:45:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4307","created_at":"2026-05-18T03:45:12Z"},{"alias_kind":"pith_short_12","alias_value":"66FF5DE26RQG","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"66FF5DE26RQGKE7V","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"66FF5DE2","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:25136def4ee400c0c47d574f1c1f5c2a4684c05aede31b8a9a7ed85a4ffa37b2","target":"graph","created_at":"2026-05-18T03:45:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let C be small category and A an arbitrary category. Consider the category C(A) whose objects are functors from C to A, and whose morphisms are natural transformations. Given a functor F : A --> B one obtains an induced functor F_C : C(A) --> C(B) . If A and B are abelian categories, we have that C(A) and C(B) are also abelian, and one has two functors R(F_C) : D(C(A)) --> D(C(B)) and (RF)_ C : C(D(A)) --> C(D (B)). The goals of this paper are: 1) to find a relationship between D (C(A)) and C(D(A)); 2) to relate the functors R(F_C) and (RF)_C. As an application, we prove a version of Mukai's T","authors_text":"Marcos Jardim, Paula Olga Gneri","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-19T16:54:44Z","title":"Derived categories of functors and Fourier--Mukai transform for quiver sheaves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4307","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4c0662516335ebe44138097f81e9b82b06c477065e01f14a17d1422d4dbce090","target":"record","created_at":"2026-05-18T03:45:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"241680d391e997a04c0178d5f35defc9917d7fe4a76fde4cb220ee71036273d7","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-19T16:54:44Z","title_canon_sha256":"30e1f5ca7f2a29dafe9aa3a196bdb4777841751e05d0548b213d3f5e145237f8"},"schema_version":"1.0","source":{"id":"1209.4307","kind":"arxiv","version":1}},"canonical_sha256":"f78a5e8c9af4606513f5a51cea9e95d1009cb225164bf1e98272f851785c3bb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f78a5e8c9af4606513f5a51cea9e95d1009cb225164bf1e98272f851785c3bb3","first_computed_at":"2026-05-18T03:45:12.925089Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:12.925089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jXR3WNcGODOhMOW4+hKq5cMf8U1vnn0CGPXMsCChOi7Mb7m4PudZlYWmWTVdQ6/G/jCGMJXoMANE21GcjfWPAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:12.925816Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.4307","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c0662516335ebe44138097f81e9b82b06c477065e01f14a17d1422d4dbce090","sha256:25136def4ee400c0c47d574f1c1f5c2a4684c05aede31b8a9a7ed85a4ffa37b2"],"state_sha256":"64574985b02e63ad698cb1118dec3bca0292ba7e512874a4daaf983da69a29d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JeUFUjtRMlxNzapDwQ8HpBfhXxVUcdqy0uXi8gzqx6wHO4LHilBrhzkjxtDVGYiiNGG/unM4tOqaMUNUvtr3DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T22:48:32.545624Z","bundle_sha256":"f7961d40ef697c371ed99e81455f99d12e72407bf342df47f37c21792e03a2c2"}}