{"title":"A characterization of differential bundles in tangent categories","authors":"Michael Ching","doi":"arxiv-2407.06515","DOIUrl":null,"url":null,"abstract":"A tangent category is a categorical abstraction of the tangent bundle\nconstruction for smooth manifolds. In that context, Cockett and Cruttwell\ndevelop the notion of differential bundle which, by work of MacAdam,\ngeneralizes the notion of smooth vector bundle to the abstract setting. Here we\nprovide a new characterization of those differential bundles and show that, up\nto isomorphism, a differential bundle is determined by its projection map and\nzero section. We show how these results can be used to quickly identify\ndifferential bundles in various tangent categories.","PeriodicalId":501135,"journal":{"name":"arXiv - MATH - Category Theory","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Category Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.06515","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
A tangent category is a categorical abstraction of the tangent bundle
construction for smooth manifolds. In that context, Cockett and Cruttwell
develop the notion of differential bundle which, by work of MacAdam,
generalizes the notion of smooth vector bundle to the abstract setting. Here we
provide a new characterization of those differential bundles and show that, up
to isomorphism, a differential bundle is determined by its projection map and
zero section. We show how these results can be used to quickly identify
differential bundles in various tangent categories.
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