{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:KRIBPROBEN4XEZCXXIAVFFXQ3D","short_pith_number":"pith:KRIBPROB","schema_version":"1.0","canonical_sha256":"545017c5c12379726457ba015296f0d8d73ba6926f43fc66a9daeb622a34f6e8","source":{"kind":"arxiv","id":"1005.0156","version":3},"attestation_state":"computed","paper":{"title":"Four problems regarding representable functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RA","authors_text":"Gigel Militaru","submitted_at":"2010-05-02T19:23:52Z","abstract_excerpt":"Let $R$, $S$ be two rings, $C$ an $R$-coring and ${}_{R}^C{\\mathcal M}$ the category of left $C$-comodules. The category ${\\bf Rep}\\, ( {}_{R}^C{\\mathcal M}, {}_{S}{\\mathcal M} )$ of all representable functors ${}_{R}^C{\\mathcal M} \\to {}_{S}{\\mathcal M}$ is shown to be equivalent to the opposite of the category ${}_{R}^C{\\mathcal M}_S$. For $U$ an $(S,R)$-bimodule we give necessary and sufficient conditions for the induction functor $U\\otimes_R - : {}_{R}^C\\mathcal{M} \\to {}_{S}\\mathcal{M}$ to be: a representable functor, an equivalence of categories, a separable or a Frobenius functor. The l"},"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":"1005.0156","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-05-02T19:23:52Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"0a22492e41a01d0f46d79f16401fe178d75dc5efaf142b9260727bcbe80abcb8","abstract_canon_sha256":"f03ba3c0664fd6c289805376f653819295c78d799b45993dafc4bb22b94c6e1f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:09.386416Z","signature_b64":"Zuv2lOAd39jATA8Yjqs7+aBRIsaPsc0n5nl1KlD3jQNRTl5JHaHyGLt6s3CIxbE6/D0bfyFvIwk6lxoXydX4Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"545017c5c12379726457ba015296f0d8d73ba6926f43fc66a9daeb622a34f6e8","last_reissued_at":"2026-05-18T02:24:09.385759Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:09.385759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Four problems regarding representable functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RA","authors_text":"Gigel Militaru","submitted_at":"2010-05-02T19:23:52Z","abstract_excerpt":"Let $R$, $S$ be two rings, $C$ an $R$-coring and ${}_{R}^C{\\mathcal M}$ the category of left $C$-comodules. The category ${\\bf Rep}\\, ( {}_{R}^C{\\mathcal M}, {}_{S}{\\mathcal M} )$ of all representable functors ${}_{R}^C{\\mathcal M} \\to {}_{S}{\\mathcal M}$ is shown to be equivalent to the opposite of the category ${}_{R}^C{\\mathcal M}_S$. For $U$ an $(S,R)$-bimodule we give necessary and sufficient conditions for the induction functor $U\\otimes_R - : {}_{R}^C\\mathcal{M} \\to {}_{S}\\mathcal{M}$ to be: a representable functor, an equivalence of categories, a separable or a Frobenius functor. The l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0156","kind":"arxiv","version":3},"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":"1005.0156","created_at":"2026-05-18T02:24:09.385836+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.0156v3","created_at":"2026-05-18T02:24:09.385836+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.0156","created_at":"2026-05-18T02:24:09.385836+00:00"},{"alias_kind":"pith_short_12","alias_value":"KRIBPROBEN4X","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"KRIBPROBEN4XEZCX","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"KRIBPROB","created_at":"2026-05-18T12:26:09.077623+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/KRIBPROBEN4XEZCXXIAVFFXQ3D","json":"https://pith.science/pith/KRIBPROBEN4XEZCXXIAVFFXQ3D.json","graph_json":"https://pith.science/api/pith-number/KRIBPROBEN4XEZCXXIAVFFXQ3D/graph.json","events_json":"https://pith.science/api/pith-number/KRIBPROBEN4XEZCXXIAVFFXQ3D/events.json","paper":"https://pith.science/paper/KRIBPROB"},"agent_actions":{"view_html":"https://pith.science/pith/KRIBPROBEN4XEZCXXIAVFFXQ3D","download_json":"https://pith.science/pith/KRIBPROBEN4XEZCXXIAVFFXQ3D.json","view_paper":"https://pith.science/paper/KRIBPROB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.0156&json=true","fetch_graph":"https://pith.science/api/pith-number/KRIBPROBEN4XEZCXXIAVFFXQ3D/graph.json","fetch_events":"https://pith.science/api/pith-number/KRIBPROBEN4XEZCXXIAVFFXQ3D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KRIBPROBEN4XEZCXXIAVFFXQ3D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KRIBPROBEN4XEZCXXIAVFFXQ3D/action/storage_attestation","attest_author":"https://pith.science/pith/KRIBPROBEN4XEZCXXIAVFFXQ3D/action/author_attestation","sign_citation":"https://pith.science/pith/KRIBPROBEN4XEZCXXIAVFFXQ3D/action/citation_signature","submit_replication":"https://pith.science/pith/KRIBPROBEN4XEZCXXIAVFFXQ3D/action/replication_record"}},"created_at":"2026-05-18T02:24:09.385836+00:00","updated_at":"2026-05-18T02:24:09.385836+00:00"}