{"title":"基于镜像序列的精确范畴的k1","authors":"C. Sherman","doi":"10.1017/IS012003019JKT187","DOIUrl":null,"url":null,"abstract":"We establish a presentation for K 1 of any small exact category P , based on the notion of “mirror image sequence,” originally introduced by Grayson in 1979; as part of the proof, we show that every element of K 1 ( P ) arises from a mirror image sequence. This provides an alternative to Nenashev's presentation in terms of “double short exact sequences.”","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"11 1","pages":"155-181"},"PeriodicalIF":0.0000,"publicationDate":"2013-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS012003019JKT187","citationCount":"2","resultStr":"{\"title\":\"K 1 of Exact Categories by Mirror Image Sequences\",\"authors\":\"C. Sherman\",\"doi\":\"10.1017/IS012003019JKT187\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We establish a presentation for K 1 of any small exact category P , based on the notion of “mirror image sequence,” originally introduced by Grayson in 1979; as part of the proof, we show that every element of K 1 ( P ) arises from a mirror image sequence. This provides an alternative to Nenashev's presentation in terms of “double short exact sequences.”\",\"PeriodicalId\":50167,\"journal\":{\"name\":\"Journal of K-Theory\",\"volume\":\"11 1\",\"pages\":\"155-181\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1017/IS012003019JKT187\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of K-Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/IS012003019JKT187\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of K-Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/IS012003019JKT187","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We establish a presentation for K 1 of any small exact category P , based on the notion of “mirror image sequence,” originally introduced by Grayson in 1979; as part of the proof, we show that every element of K 1 ( P ) arises from a mirror image sequence. This provides an alternative to Nenashev's presentation in terms of “double short exact sequences.”
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