{"paper":{"title":"Excellent metrics on triangulated categories, and the involutivity of the map taking $\\mathcal{S}$ to $\\mathfrak{S}({\\mathcal{S})^{\\mathrm{op}}}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT"],"primary_cat":"math.CT","authors_text":"Amnon Neeman","submitted_at":"2025-05-14T04:07:57Z","abstract_excerpt":"In the article arXiv:1806.06471 we defined good metrics on triangulated categories, and then studied the construction, that began with a triangulated category $\\mathcal{S}$ together with a good metric $\\{\\mathcal{M}_i,\\,i\\in\\mathbb{N}\\}$, and out of it cooked up another triangulated category $\\mathfrak(\\mathcal{S})$. We went on to study examples, and produced many for which the construction is involutive. By this we mean that, if you let $\\mathcal{T}=\\mathfrak{S}(\\mathcal{S})^{\\mathrm{op}}$, then there is a choice of metric on $\\mathcal{T}$ for which $\\mathcal{S}=\\mathfrak{S}(\\mathcal{T})^{\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.09120","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.09120/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}