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Here dim(C)=sum_i d(X_i)^2, the X_i being the simple objects. We prove the following double centralizer theorem: Let C be a modular category and K a full tensor subcategory closed w.r.t. direct sums, subobjects and "},"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/0201017","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CT","submitted_at":"2002-01-03T16:59:50Z","cross_cats_sorted":[],"title_canon_sha256":"0374e52e1e9c835ce268942deaaa7c2635430b67d9f24b059ec94f4e6bdb47e5","abstract_canon_sha256":"06902a360c1ac3fe82a9907ec96258703ac3fbe22086a190d2f411e6ba7fc06c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:35:50.758745Z","signature_b64":"FfYrRRq2Iduby493HXLZf5m0+oO+1VdNzlzUEIL8myvlAsaSXMzZ7COi7jFU/Sr3jkojBadshtFfdrWpOGpZAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56c356302df051e2b6edaee0dd36fcc609b9d1013be84457637259fc560e8834","last_reissued_at":"2026-07-04T14:35:50.758391Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:35:50.758391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Structure of Modular Categories","license":"","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Michael Mueger","submitted_at":"2002-01-03T16:59:50Z","abstract_excerpt":"For a braided tensor category C and a subcategory K there is a notion of centralizer C_C(K), which is a full tensor subcategory of C. 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