{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:BQJBEJCPGLEYWC7IBVZ4DQVSVP","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":"d9b1a9fe95646a00fe1aa453ebdc136acb741847312dfeac9a6b07c08d557089","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2020-11-05T18:49:24Z","title_canon_sha256":"91c03bf17decd16b781d95a7f7a9847f2734a4eff92b231ba756b8d412c1c212"},"schema_version":"1.0","source":{"id":"2011.03035","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.03035","created_at":"2026-07-05T01:49:33Z"},{"alias_kind":"arxiv_version","alias_value":"2011.03035v1","created_at":"2026-07-05T01:49:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.03035","created_at":"2026-07-05T01:49:33Z"},{"alias_kind":"pith_short_12","alias_value":"BQJBEJCPGLEY","created_at":"2026-07-05T01:49:33Z"},{"alias_kind":"pith_short_16","alias_value":"BQJBEJCPGLEYWC7I","created_at":"2026-07-05T01:49:33Z"},{"alias_kind":"pith_short_8","alias_value":"BQJBEJCP","created_at":"2026-07-05T01:49:33Z"}],"graph_snapshots":[{"event_id":"sha256:2ef65455054c17ac9d3b360542a1d1df200183312238c24851e9ccbfca20cf6e","target":"graph","created_at":"2026-07-05T01:49:33Z","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/2011.03035/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define for each $n \\geq 1$ a symmetric monoidal $(\\infty, n+1)$-category $n\\mathrm{Pr}^L$ whose objects we call presentable $(\\infty,n)$-categories, generalizing the usual theory of presentable $(\\infty,1)$-categories. We show that each object $\\mathcal{C}$ in $n\\mathrm{Pr}^L$ has an underlying $(\\infty,n)$-category $\\psi_n(\\mathcal{C})$ which admits all conical colimits, and that conical colimits of right adjointable diagrams in $\\psi_n(\\mathcal{C})$ can be computed in terms of conical limits after passage to right adjoints.","authors_text":"Germ\\'an Stefanich","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2020-11-05T18:49:24Z","title":"Presentable $(\\infty, n)$-categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.03035","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:c804c94f1a378243e39c8a1e0d7393f2e6957c131fa8168f7a60e9d205c02304","target":"record","created_at":"2026-07-05T01:49:33Z","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":"d9b1a9fe95646a00fe1aa453ebdc136acb741847312dfeac9a6b07c08d557089","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2020-11-05T18:49:24Z","title_canon_sha256":"91c03bf17decd16b781d95a7f7a9847f2734a4eff92b231ba756b8d412c1c212"},"schema_version":"1.0","source":{"id":"2011.03035","kind":"arxiv","version":1}},"canonical_sha256":"0c1212244f32c98b0be80d73c1c2b2abd6a1b50e158312a12e5e96407e3f6c4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c1212244f32c98b0be80d73c1c2b2abd6a1b50e158312a12e5e96407e3f6c4c","first_computed_at":"2026-07-05T01:49:33.373034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:49:33.373034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"05Tg8aeZJCPUASYfyQAuP1XqRu89iQLn+i2M/CsJL8yCK/9dxu67jSFiGL+sywgwc+tH6ISid6Eo/BuIiAU6Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:49:33.373530Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.03035","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c804c94f1a378243e39c8a1e0d7393f2e6957c131fa8168f7a60e9d205c02304","sha256:2ef65455054c17ac9d3b360542a1d1df200183312238c24851e9ccbfca20cf6e"],"state_sha256":"8d0e2ac4b4a9464c15fcec6af207b3ae5e2080b29e9e9c808c40eb827f850f04"}