{"title":"无指向同调类别的代数 $K_0$","authors":"Felix Küng","doi":"arxiv-2407.20911","DOIUrl":null,"url":null,"abstract":"We introduce the notion of Grothendieck heaps for unpointed Waldhausen\ncategories and unpointed stable $\\infty$-categories. This allows an extension\nof the studies of $\\mathrm{K}_0$ to the homotopy category of unpointed\ntopological spaces.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"76 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Algebraic $K_0$ for unpointed homotopy Categories\",\"authors\":\"Felix Küng\",\"doi\":\"arxiv-2407.20911\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce the notion of Grothendieck heaps for unpointed Waldhausen\\ncategories and unpointed stable $\\\\infty$-categories. This allows an extension\\nof the studies of $\\\\mathrm{K}_0$ to the homotopy category of unpointed\\ntopological spaces.\",\"PeriodicalId\":501143,\"journal\":{\"name\":\"arXiv - MATH - K-Theory and Homology\",\"volume\":\"76 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - K-Theory and Homology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2407.20911\",\"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 - K-Theory and Homology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.20911","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We introduce the notion of Grothendieck heaps for unpointed Waldhausen
categories and unpointed stable $\infty$-categories. This allows an extension
of the studies of $\mathrm{K}_0$ to the homotopy category of unpointed
topological spaces.
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