{"title":"On constructing weight structures and extending them to idempotent extensions","authors":"M. Bondarko, V. Sosnilo","doi":"10.4310/HHA.2018.V20.N1.A3","DOIUrl":null,"url":null,"abstract":"We describe a new method for constructing a weight structure $w$ on a triangulated category $C$. \nFor a given $C$ and $w$ it allow us to give a fairly comprehensive (and new) description of those triangulated categories consisting of retracts of objects of $C$ (i.e., of subcategories of the Karoubi envelope of $C$ that contain $C$; we call them idempotent extensions of $C$) such that $w$ extends to them. In particular, any bounded above or below $w$ extends to any idempotent extension of $C$. We also discuss the applications of our results to certain triangulated categories of (\"relative\") motives.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2016-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"30","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: K-Theory and Homology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/HHA.2018.V20.N1.A3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 30
Abstract
We describe a new method for constructing a weight structure $w$ on a triangulated category $C$.
For a given $C$ and $w$ it allow us to give a fairly comprehensive (and new) description of those triangulated categories consisting of retracts of objects of $C$ (i.e., of subcategories of the Karoubi envelope of $C$ that contain $C$; we call them idempotent extensions of $C$) such that $w$ extends to them. In particular, any bounded above or below $w$ extends to any idempotent extension of $C$. We also discuss the applications of our results to certain triangulated categories of ("relative") motives.