{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:3H2B2XF4IDLHZXGU2OQMQHTAXS","short_pith_number":"pith:3H2B2XF4","schema_version":"1.0","canonical_sha256":"d9f41d5cbc40d67cdcd4d3a0c81e60bcbf6d656676f5fe154e11e8e494ced21d","source":{"kind":"arxiv","id":"1303.6875","version":1},"attestation_state":"computed","paper":{"title":"Fused Mackey functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RA"],"primary_cat":"math.GR","authors_text":"Serge Bouc (LAMFA)","submitted_at":"2013-03-27T16:17:01Z","abstract_excerpt":"Let $G$ be a finite group. In [HTW], Hambleton, Taylor and Williams have considered the question of comparing Mackey functors for $G$ and biset functors defined on subgroups of $G$ and bifree bisets as morphisms. This paper proposes a different approach to this problem, from the point of view of various categories of $G$-sets. In particular, the category of fused $G$-sets is introduced, as well its category of spans. The fused Mackey functors for $G$ over a commutative ring $R$ are defined as $R$-linear functors from this ($R$-linearized) category of spans to $R$-modules. They form an abelian "},"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":"1303.6875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-03-27T16:17:01Z","cross_cats_sorted":["math.CT","math.RA"],"title_canon_sha256":"34772d9f6bb43c16a8d08db4d2b11a829a734c576b8557c94c939a4e55859233","abstract_canon_sha256":"1f4f74d177429385d89d5a5a515162cee420fafa1440bf6c55d6162833f7b908"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:39.509931Z","signature_b64":"XlW8tJYRP9PEm+A06PW+UCUhKKTvrB7WpBtTE2VVRi1fxD96xYLWLGBm3Mg9c5F38nYPxaRKebQVzcWRyrofDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9f41d5cbc40d67cdcd4d3a0c81e60bcbf6d656676f5fe154e11e8e494ced21d","last_reissued_at":"2026-05-18T03:29:39.509156Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:39.509156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fused Mackey functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RA"],"primary_cat":"math.GR","authors_text":"Serge Bouc (LAMFA)","submitted_at":"2013-03-27T16:17:01Z","abstract_excerpt":"Let $G$ be a finite group. In [HTW], Hambleton, Taylor and Williams have considered the question of comparing Mackey functors for $G$ and biset functors defined on subgroups of $G$ and bifree bisets as morphisms. This paper proposes a different approach to this problem, from the point of view of various categories of $G$-sets. In particular, the category of fused $G$-sets is introduced, as well its category of spans. The fused Mackey functors for $G$ over a commutative ring $R$ are defined as $R$-linear functors from this ($R$-linearized) category of spans to $R$-modules. They form an abelian "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6875","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":""},"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":"1303.6875","created_at":"2026-05-18T03:29:39.509280+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.6875v1","created_at":"2026-05-18T03:29:39.509280+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6875","created_at":"2026-05-18T03:29:39.509280+00:00"},{"alias_kind":"pith_short_12","alias_value":"3H2B2XF4IDLH","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3H2B2XF4IDLHZXGU","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3H2B2XF4","created_at":"2026-05-18T12:27:32.513160+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/3H2B2XF4IDLHZXGU2OQMQHTAXS","json":"https://pith.science/pith/3H2B2XF4IDLHZXGU2OQMQHTAXS.json","graph_json":"https://pith.science/api/pith-number/3H2B2XF4IDLHZXGU2OQMQHTAXS/graph.json","events_json":"https://pith.science/api/pith-number/3H2B2XF4IDLHZXGU2OQMQHTAXS/events.json","paper":"https://pith.science/paper/3H2B2XF4"},"agent_actions":{"view_html":"https://pith.science/pith/3H2B2XF4IDLHZXGU2OQMQHTAXS","download_json":"https://pith.science/pith/3H2B2XF4IDLHZXGU2OQMQHTAXS.json","view_paper":"https://pith.science/paper/3H2B2XF4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.6875&json=true","fetch_graph":"https://pith.science/api/pith-number/3H2B2XF4IDLHZXGU2OQMQHTAXS/graph.json","fetch_events":"https://pith.science/api/pith-number/3H2B2XF4IDLHZXGU2OQMQHTAXS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3H2B2XF4IDLHZXGU2OQMQHTAXS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3H2B2XF4IDLHZXGU2OQMQHTAXS/action/storage_attestation","attest_author":"https://pith.science/pith/3H2B2XF4IDLHZXGU2OQMQHTAXS/action/author_attestation","sign_citation":"https://pith.science/pith/3H2B2XF4IDLHZXGU2OQMQHTAXS/action/citation_signature","submit_replication":"https://pith.science/pith/3H2B2XF4IDLHZXGU2OQMQHTAXS/action/replication_record"}},"created_at":"2026-05-18T03:29:39.509280+00:00","updated_at":"2026-05-18T03:29:39.509280+00:00"}