{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2002:F4T366MYYJOPOGO5ZG23UIBSQU","short_pith_number":"pith:F4T366MY","schema_version":"1.0","canonical_sha256":"2f27bf7998c25cf719ddc9b5ba2032853609940ae5f47f12d7ba5c5f321000a8","source":{"kind":"arxiv","id":"math-ph/0211067","version":1},"attestation_state":"computed","paper":{"title":"Method of Additional Structures on the Objects of a Monoidal Kleisli Category as a Background for Information Transformers Theory","license":"","headline":"","cross_cats":["cs.MA","math.CT","math.MP"],"primary_cat":"math-ph","authors_text":"P. V. Golubtsov, S. S. Moskaliuk","submitted_at":"2002-11-27T18:47:30Z","abstract_excerpt":"Category theory provides a compact method of encoding mathematical structures in a uniform way, thereby enabling the use of general theorems on, for example, equivalence and universal constructions. In this article we develop the method of additional structures on the objects of a monoidal Kleisli category. It is proposed to consider any uniform class of information transformers (ITs) as a family of morphisms of a category that satisfy certain set of axioms. This makes it possible to study in a uniform way different types of ITs, e.g., statistical, multivalued, and fuzzy ITs. Proposed axioms d"},"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":"math-ph/0211067","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-11-27T18:47:30Z","cross_cats_sorted":["cs.MA","math.CT","math.MP"],"title_canon_sha256":"60001b2ebbbdc0ac13e07e7c2c2feaa0d8eb11fb85aae5bb70e75ef3f3c04110","abstract_canon_sha256":"42f40fbc8cb781dcbec32d4503f51547a44249c5863f2e712b0df02f4fecafd5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:33:45.697165Z","signature_b64":"ZpHAH4hdiuNZUCx45ZvZ7QZblKDAVYlmdo6omMJepeYI7cA/THOeW80lTTPN2IjqGGyfRENHp3YOHHreMHd/DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f27bf7998c25cf719ddc9b5ba2032853609940ae5f47f12d7ba5c5f321000a8","last_reissued_at":"2026-07-04T14:33:45.696774Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:33:45.696774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Method of Additional Structures on the Objects of a Monoidal Kleisli Category as a Background for Information Transformers Theory","license":"","headline":"","cross_cats":["cs.MA","math.CT","math.MP"],"primary_cat":"math-ph","authors_text":"P. V. Golubtsov, S. S. Moskaliuk","submitted_at":"2002-11-27T18:47:30Z","abstract_excerpt":"Category theory provides a compact method of encoding mathematical structures in a uniform way, thereby enabling the use of general theorems on, for example, equivalence and universal constructions. In this article we develop the method of additional structures on the objects of a monoidal Kleisli category. It is proposed to consider any uniform class of information transformers (ITs) as a family of morphisms of a category that satisfy certain set of axioms. This makes it possible to study in a uniform way different types of ITs, e.g., statistical, multivalued, and fuzzy ITs. Proposed axioms d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0211067","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0211067/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"math-ph/0211067","created_at":"2026-07-04T14:33:45.696835+00:00"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0211067v1","created_at":"2026-07-04T14:33:45.696835+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0211067","created_at":"2026-07-04T14:33:45.696835+00:00"},{"alias_kind":"pith_short_12","alias_value":"F4T366MYYJOP","created_at":"2026-07-04T14:33:45.696835+00:00"},{"alias_kind":"pith_short_16","alias_value":"F4T366MYYJOPOGO5","created_at":"2026-07-04T14:33:45.696835+00:00"},{"alias_kind":"pith_short_8","alias_value":"F4T366MY","created_at":"2026-07-04T14:33:45.696835+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.07021","citing_title":"A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics","ref_index":57,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/F4T366MYYJOPOGO5ZG23UIBSQU","json":"https://pith.science/pith/F4T366MYYJOPOGO5ZG23UIBSQU.json","graph_json":"https://pith.science/api/pith-number/F4T366MYYJOPOGO5ZG23UIBSQU/graph.json","events_json":"https://pith.science/api/pith-number/F4T366MYYJOPOGO5ZG23UIBSQU/events.json","paper":"https://pith.science/paper/F4T366MY"},"agent_actions":{"view_html":"https://pith.science/pith/F4T366MYYJOPOGO5ZG23UIBSQU","download_json":"https://pith.science/pith/F4T366MYYJOPOGO5ZG23UIBSQU.json","view_paper":"https://pith.science/paper/F4T366MY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math-ph/0211067&json=true","fetch_graph":"https://pith.science/api/pith-number/F4T366MYYJOPOGO5ZG23UIBSQU/graph.json","fetch_events":"https://pith.science/api/pith-number/F4T366MYYJOPOGO5ZG23UIBSQU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F4T366MYYJOPOGO5ZG23UIBSQU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F4T366MYYJOPOGO5ZG23UIBSQU/action/storage_attestation","attest_author":"https://pith.science/pith/F4T366MYYJOPOGO5ZG23UIBSQU/action/author_attestation","sign_citation":"https://pith.science/pith/F4T366MYYJOPOGO5ZG23UIBSQU/action/citation_signature","submit_replication":"https://pith.science/pith/F4T366MYYJOPOGO5ZG23UIBSQU/action/replication_record"}},"created_at":"2026-07-04T14:33:45.696835+00:00","updated_at":"2026-07-04T14:33:45.696835+00:00"}