{"paper":{"title":"Tangent Ind-Categories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Geoff Vooys","submitted_at":"2023-07-17T01:17:13Z","abstract_excerpt":"In this paper we show that if $\\mathscr{C}$ is a tangent category then the Ind-category $\\operatorname{Ind}(\\mathscr{C})$ is a tangent category as well with a tangent structure which locally looks like the tangent structure on $\\mathscr{C}$. Afterwards we give a pseudolimit description of $\\operatorname{Ind}(\\mathscr{C})_{/X}$ when $\\mathscr{C}$ admits finite products, show that the $\\operatorname{Ind}$-tangent category of a representable tangent category remains representable (in the sense that it has a microlinear object), and we characterize the differential bundles in $\\operatorname{Ind}(\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.08183","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/2307.08183/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"}