{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:V4DM2DTPBJ52Z53E2T3MFFNXZL","short_pith_number":"pith:V4DM2DTP","schema_version":"1.0","canonical_sha256":"af06cd0e6f0a7bacf764d4f6c295b7caf407382ecb6c836bd0d750c0c831565d","source":{"kind":"arxiv","id":"1705.03863","version":3},"attestation_state":"computed","paper":{"title":"Gabriel-Morita theory for excisive model categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Clemens Berger, Kruna Ratkovic","submitted_at":"2017-05-10T17:27:43Z","abstract_excerpt":"We develop a Gabriel-Morita theory for strong monads on pointed monoidal model categories. Assuming that the model category is excisive, i.e. the derived suspension functor is conservative, we show that if the monad T preserves cofibre sequences up to homotopy and has a weakly invertible strength, then the category of T-algebras is Quillen equivalent to the category of T(I)-modules where I is the monoidal unit. This recovers Schwede's theorem on connective stable homotopy over a pointed Lawvere theory as special case."},"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":"1705.03863","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-05-10T17:27:43Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"e9a47df495c2b63fd5c631173843627c1f5351cdbf1db523ec9bcd51628d0266","abstract_canon_sha256":"81779d3cda0b3305ae280fd1a61b4ee00d38fa47c39859140862a99e71466763"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:25.726549Z","signature_b64":"DMUfuyxjniqJzdkpDvD2UPpxKUmODr54K0g3mb5Fsc8MU2b2kJ2W+NccCsF+Dnj5sax/vc+Ikh1jBWQX/5grCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af06cd0e6f0a7bacf764d4f6c295b7caf407382ecb6c836bd0d750c0c831565d","last_reissued_at":"2026-05-18T00:32:25.725898Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:25.725898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gabriel-Morita theory for excisive model categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Clemens Berger, Kruna Ratkovic","submitted_at":"2017-05-10T17:27:43Z","abstract_excerpt":"We develop a Gabriel-Morita theory for strong monads on pointed monoidal model categories. Assuming that the model category is excisive, i.e. the derived suspension functor is conservative, we show that if the monad T preserves cofibre sequences up to homotopy and has a weakly invertible strength, then the category of T-algebras is Quillen equivalent to the category of T(I)-modules where I is the monoidal unit. This recovers Schwede's theorem on connective stable homotopy over a pointed Lawvere theory as special case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03863","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":"1705.03863","created_at":"2026-05-18T00:32:25.725988+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.03863v3","created_at":"2026-05-18T00:32:25.725988+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03863","created_at":"2026-05-18T00:32:25.725988+00:00"},{"alias_kind":"pith_short_12","alias_value":"V4DM2DTPBJ52","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"V4DM2DTPBJ52Z53E","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"V4DM2DTP","created_at":"2026-05-18T12:31:49.984773+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/V4DM2DTPBJ52Z53E2T3MFFNXZL","json":"https://pith.science/pith/V4DM2DTPBJ52Z53E2T3MFFNXZL.json","graph_json":"https://pith.science/api/pith-number/V4DM2DTPBJ52Z53E2T3MFFNXZL/graph.json","events_json":"https://pith.science/api/pith-number/V4DM2DTPBJ52Z53E2T3MFFNXZL/events.json","paper":"https://pith.science/paper/V4DM2DTP"},"agent_actions":{"view_html":"https://pith.science/pith/V4DM2DTPBJ52Z53E2T3MFFNXZL","download_json":"https://pith.science/pith/V4DM2DTPBJ52Z53E2T3MFFNXZL.json","view_paper":"https://pith.science/paper/V4DM2DTP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.03863&json=true","fetch_graph":"https://pith.science/api/pith-number/V4DM2DTPBJ52Z53E2T3MFFNXZL/graph.json","fetch_events":"https://pith.science/api/pith-number/V4DM2DTPBJ52Z53E2T3MFFNXZL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V4DM2DTPBJ52Z53E2T3MFFNXZL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V4DM2DTPBJ52Z53E2T3MFFNXZL/action/storage_attestation","attest_author":"https://pith.science/pith/V4DM2DTPBJ52Z53E2T3MFFNXZL/action/author_attestation","sign_citation":"https://pith.science/pith/V4DM2DTPBJ52Z53E2T3MFFNXZL/action/citation_signature","submit_replication":"https://pith.science/pith/V4DM2DTPBJ52Z53E2T3MFFNXZL/action/replication_record"}},"created_at":"2026-05-18T00:32:25.725988+00:00","updated_at":"2026-05-18T00:32:25.725988+00:00"}