{"title":"Local Rigidity and Six Functor Formalisms","authors":"Adrian Clough","doi":"arxiv-2408.07564","DOIUrl":null,"url":null,"abstract":"The coefficient categories of six functor formalisms are often locally rigid,\nand when this is the case, the exceptional pushforward and pullback adjunctions\nmay be defined formally. In this short note it is shown that for f a proper map\nresp. an open embedding the well known formulas f_! = f_* resp. f_! = f_# may\nlikewise be deduced formally.","PeriodicalId":501135,"journal":{"name":"arXiv - MATH - Category Theory","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-14","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-2408.07564","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
The coefficient categories of six functor formalisms are often locally rigid,
and when this is the case, the exceptional pushforward and pullback adjunctions
may be defined formally. In this short note it is shown that for f a proper map
resp. an open embedding the well known formulas f_! = f_* resp. f_! = f_# may
likewise be deduced formally.
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