{"paper":{"title":"The category of centralizer lattices of groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Centralizer-respecting homomorphisms form a category that maps via functor to centralizer lattices of groups.","cross_cats":[],"primary_cat":"math.GR","authors_text":"Mark L. Lewis, Ryan McCulloch, William Cocke","submitted_at":"2026-05-13T20:27:15Z","abstract_excerpt":"We formalize the concept of a centralizer-respecting homomorphism, surjective homomorphisms which are equivariant with respect to taking the centralizer of a subgroup. There is a functor from the category of centralizer-respecting homomorphisms to the category of centralizer lattices. Finally, we conclude with some theorems about centralizer-respecting homomorphisms that show that the category of centralizer-respecting homomorphisms has many interesting maps."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"There is a functor from the category of centralizer-respecting homomorphisms to the category of centralizer lattices.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the proposed definition of centralizer-respecting homomorphism yields a well-defined category and that the centralizer operation interacts with the homomorphism in a way that produces a valid functor.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Introduces centralizer-respecting homomorphisms between groups and a functor from their category to the category of centralizer lattices.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Centralizer-respecting homomorphisms form a category that maps via functor to centralizer lattices of groups.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"71e575ec72c4d9ee10cb5ed720c16507ba7518218c0521969095354864ef7eac"},"source":{"id":"2605.14095","kind":"arxiv","version":1},"verdict":{"id":"aaef8ade-f13b-43ef-b902-a03d50a59f17","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:12:42.309329Z","strongest_claim":"There is a functor from the category of centralizer-respecting homomorphisms to the category of centralizer lattices.","one_line_summary":"Introduces centralizer-respecting homomorphisms between groups and a functor from their category to the category of centralizer lattices.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the proposed definition of centralizer-respecting homomorphism yields a well-defined category and that the centralizer operation interacts with the homomorphism in a way that produces a valid functor.","pith_extraction_headline":"Centralizer-respecting homomorphisms form a category that maps via functor to centralizer lattices of groups."},"references":{"count":9,"sample":[{"doi":"","year":1994,"title":"Subgroup lattices of groups , author=. 1994 , publisher=","work_id":"63855442-9203-4b08-9c62-373404f5b0b6","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2012,"title":"Structure of a group and the structure of its lattice of subgroups , author=. 2012 , publisher=","work_id":"753e9a42-2a6f-4bbc-b97c-46b8190c5669","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"Exploring the","work_id":"2eb49f11-3b5b-4683-99a6-8b9380d04e94","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2026,"title":"Finite groups with few subgroups not in the","work_id":"b0fb4e5b-6f10-4f98-b5cb-17fb472ab8e4","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2026,"title":"Bulletin of the Australian Mathematical Society , author=","work_id":"d00fcf8c-d74e-47c6-b517-a2d5be1d796b","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":9,"snapshot_sha256":"ab1a0ce9417c0e746fa95f4eb450b4cc4d344a7f63874bf69ddbb1af814fa07f","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"b6b57cb60835e99b4154bf8ad5180e7dd7d874a3adf15afc64d91ae4425a300d"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}