{"title":"EXACT SUBCATEGORIES, SUBFUNCTORS OF , AND SOME APPLICATIONS","authors":"HAILONG DAO, SOUVIK DEY, MONALISA DUTTA","doi":"10.1017/nmj.2023.29","DOIUrl":null,"url":null,"abstract":"Abstract Let $({\\cal{A}},{\\cal{E}})$ be an exact category. We establish basic results that allow one to identify sub(bi)functors of ${\\operatorname{Ext}}_{\\cal{E}}(-,-)$ using additivity of numerical functions and restriction to subcategories. We also study a small number of these new functors over commutative local rings in detail and find a range of applications from detecting regularity to understanding Ulrich modules.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/nmj.2023.29","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
Abstract Let $({\cal{A}},{\cal{E}})$ be an exact category. We establish basic results that allow one to identify sub(bi)functors of ${\operatorname{Ext}}_{\cal{E}}(-,-)$ using additivity of numerical functions and restriction to subcategories. We also study a small number of these new functors over commutative local rings in detail and find a range of applications from detecting regularity to understanding Ulrich modules.
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