局部刚度和六个矢量形式主义

arXiv - MATH - Category Theory Pub Date : 2024-08-14 DOI:arxiv-2408.07564

Adrian Clough

{"title":"局部刚度和六个矢量形式主义","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":"{\"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}","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

摘要

六个函数形式的系数范畴通常是局部刚性的，在这种情况下，可以正式定义特殊的前推和回拉谓词。在这篇短文中，我们将证明，对于 f 一个适当的映射对应于一个开放的嵌入，众所周知的公式 f_！= f_* resp！= f_#同样可以正式推导出来。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Local Rigidity and Six Functor Formalisms

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Category Theory

自引率

0.00%

发文量