{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:OGPAA2BXCNJ2RQTO5HQIVF77VD","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":"6753eecb25136bf08d848866b976734777dcb6d6cece98d4ad5c6a983f8965c2","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2024-04-05T09:11:43Z","title_canon_sha256":"590d86e362fb3ddc1c6714868385b3675068c27490f7b7dce19e2f2380cad3cd"},"schema_version":"1.0","source":{"id":"2404.03971","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.03971","created_at":"2026-07-05T08:04:43Z"},{"alias_kind":"arxiv_version","alias_value":"2404.03971v1","created_at":"2026-07-05T08:04:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.03971","created_at":"2026-07-05T08:04:43Z"},{"alias_kind":"pith_short_12","alias_value":"OGPAA2BXCNJ2","created_at":"2026-07-05T08:04:43Z"},{"alias_kind":"pith_short_16","alias_value":"OGPAA2BXCNJ2RQTO","created_at":"2026-07-05T08:04:43Z"},{"alias_kind":"pith_short_8","alias_value":"OGPAA2BX","created_at":"2026-07-05T08:04:43Z"}],"graph_snapshots":[{"event_id":"sha256:eca560325766bdd5ce63e1f44acbc898bfbbdf27dc6e85506ec40cee69f5d39f","target":"graph","created_at":"2026-07-05T08:04:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.03971/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove an unstraightening result for lax transformations between functors from an arbitrary $(\\infty,2)$-category to that of $(\\infty,2)$-categories. We apply this to study partially (op)lax and weighted (co)limits, giving fibrational descriptions of such (co)limits for diagrams valued in $(\\infty,2)$-categories, to characterize adjoints in $(\\infty,2)$-categories of functors and (op)lax transformations, and to prove a mate correspondence between lax transformations that are componentwise right adjoints and oplax transformations that are componentwise left adjoints, for such transformations ","authors_text":"Andrea Gagna, Fernando Abell\\'an, Rune Haugseng","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2024-04-05T09:11:43Z","title":"Straightening for lax transformations and adjunctions of $(\\infty,2)$-categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.03971","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":"sha256:028e9da938b5689c307875e0c9713dd99f11ee4a99c6794004660c28fd2b7fc7","target":"record","created_at":"2026-07-05T08:04:43Z","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":"6753eecb25136bf08d848866b976734777dcb6d6cece98d4ad5c6a983f8965c2","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2024-04-05T09:11:43Z","title_canon_sha256":"590d86e362fb3ddc1c6714868385b3675068c27490f7b7dce19e2f2380cad3cd"},"schema_version":"1.0","source":{"id":"2404.03971","kind":"arxiv","version":1}},"canonical_sha256":"719e0068371353a8c26ee9e08a97ffa8f180bf9837451bc1dcc8688a6998b764","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"719e0068371353a8c26ee9e08a97ffa8f180bf9837451bc1dcc8688a6998b764","first_computed_at":"2026-07-05T08:04:43.748192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:04:43.748192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rPTRXlbOCdy0Jxf0AoIwVaXok4YIMMDzf9jLUYBBIKWEr7COFv7PilL0dS5nP2QFj/zlihqtORFH1LWY8c3yBw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:04:43.748651Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.03971","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:028e9da938b5689c307875e0c9713dd99f11ee4a99c6794004660c28fd2b7fc7","sha256:eca560325766bdd5ce63e1f44acbc898bfbbdf27dc6e85506ec40cee69f5d39f"],"state_sha256":"51cc1ce76dadf07679ff42cc30bc3b64672659740d7e0da00f37207ac38114db"}