{"title":"Wakamatsu tilting subcategories and weak support tau-tilting subcategories in recollement","authors":"Yongduo Wang, Hongyang Luo, Jian He, Dejun Wu","doi":"arxiv-2409.07026","DOIUrl":null,"url":null,"abstract":"In this article, we prove that if (A, B, C) is a recollement of abelian\ncategories, then wakamatsu tilting (resp. weak support tau-tilting)\nsubcategories in A and C can induce wakamatsu tilting (resp. weak support\ntau-tilting) subcategories in B, and the converses hold under natural\nassumptions. As an application, we mainly consider the relationship of\ntau-cotorsion torsion triples in (A, B, C).","PeriodicalId":501038,"journal":{"name":"arXiv - MATH - Representation Theory","volume":"23 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Representation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.07026","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
In this article, we prove that if (A, B, C) is a recollement of abelian
categories, then wakamatsu tilting (resp. weak support tau-tilting)
subcategories in A and C can induce wakamatsu tilting (resp. weak support
tau-tilting) subcategories in B, and the converses hold under natural
assumptions. As an application, we mainly consider the relationship of
tau-cotorsion torsion triples in (A, B, C).
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