{"title":"微分向量空间的同调代数","authors":"Enxin Wu","doi":"10.4310/HHA.2015.V17.N1.A17","DOIUrl":null,"url":null,"abstract":"Diffeological spaces are natural generalizations of smooth manifolds, introduced by J.M.~Souriau and his mathematical group in the 1980's. Diffeological vector spaces (especially fine diffeological vector spaces) were first used by P. Iglesias-Zemmour to model some infinite dimensional spaces in~\\cite{I1,I2}. K.~Costello and O.~Gwilliam developed homological algebra for differentiable diffeological vector spaces in Appendix A of their book~\\cite{CG}. In this paper, we present homological algebra of general diffeological vector spaces via the projective objects with respect to all linear subductions, together with some applications in analysis.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2014-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"27","resultStr":"{\"title\":\"Homological Algebra for Diffeological Vector Spaces\",\"authors\":\"Enxin Wu\",\"doi\":\"10.4310/HHA.2015.V17.N1.A17\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Diffeological spaces are natural generalizations of smooth manifolds, introduced by J.M.~Souriau and his mathematical group in the 1980's. Diffeological vector spaces (especially fine diffeological vector spaces) were first used by P. Iglesias-Zemmour to model some infinite dimensional spaces in~\\\\cite{I1,I2}. K.~Costello and O.~Gwilliam developed homological algebra for differentiable diffeological vector spaces in Appendix A of their book~\\\\cite{CG}. In this paper, we present homological algebra of general diffeological vector spaces via the projective objects with respect to all linear subductions, together with some applications in analysis.\",\"PeriodicalId\":309711,\"journal\":{\"name\":\"arXiv: K-Theory and Homology\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"27\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: K-Theory and Homology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4310/HHA.2015.V17.N1.A17\",\"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: K-Theory and Homology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/HHA.2015.V17.N1.A17","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Homological Algebra for Diffeological Vector Spaces
Diffeological spaces are natural generalizations of smooth manifolds, introduced by J.M.~Souriau and his mathematical group in the 1980's. Diffeological vector spaces (especially fine diffeological vector spaces) were first used by P. Iglesias-Zemmour to model some infinite dimensional spaces in~\cite{I1,I2}. K.~Costello and O.~Gwilliam developed homological algebra for differentiable diffeological vector spaces in Appendix A of their book~\cite{CG}. In this paper, we present homological algebra of general diffeological vector spaces via the projective objects with respect to all linear subductions, together with some applications in analysis.
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