{"title":"Homotopy Type Theory: The Logic of Space","authors":"Michael Shulman","doi":"10.1017/9781108854429.009","DOIUrl":"https://doi.org/10.1017/9781108854429.009","url":null,"abstract":"This is an introduction to type theory, synthetic topology, and homotopy type theory from a category-theoretic and topological point of view, written as a chapter for the book \"New Spaces for Mathematics and Physics\" (ed. Gabriel Catren and Mathieu Anel).","PeriodicalId":340802,"journal":{"name":"New Spaces in Mathematics","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115829358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Microlocal Analysis and Beyond","authors":"P. Schapira","doi":"10.1017/9781108854429.005","DOIUrl":"https://doi.org/10.1017/9781108854429.005","url":null,"abstract":"We shall explain how the idea of microlocal analysis of the seventies has been reformulated in the framework of sheaf theory in the eighties and then applied to various branches of mathematics, such as linear partial differential equations or symplectic topology.","PeriodicalId":340802,"journal":{"name":"New Spaces in Mathematics","volume":"96 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116424089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"New Methods forOld Spaces: Synthetic Differential Geometry","authors":"A. Kock","doi":"10.1017/9781108854429.004","DOIUrl":"https://doi.org/10.1017/9781108854429.004","url":null,"abstract":"Survey talk on certain aspects of the subject, stressing the neighbor relation as a basic notion in differential geometry.","PeriodicalId":340802,"journal":{"name":"New Spaces in Mathematics","volume":"4604 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126519702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Differential Geometry","authors":"Lia Vaš","doi":"10.1017/9781108854429.002","DOIUrl":"https://doi.org/10.1017/9781108854429.002","url":null,"abstract":"The terms xij, i, j = 1, 2 can be represented as a linear combination of tangential and normal component. Each of the vectors xij can be represented as a combination of the tangent component (which itself is a combination of vectors x1 and x2) and the normal component (which is a multiple of the unit normal vector n). Let Γij and Γ 2 ij denote the coefficients of the tangent component and Lij denote the coefficient with n of vector xij. Thus,","PeriodicalId":340802,"journal":{"name":"New Spaces in Mathematics","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134603642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stacks","authors":"N. Mestrano, Carlos Simpson","doi":"10.1017/9781108854429.012","DOIUrl":"https://doi.org/10.1017/9781108854429.012","url":null,"abstract":"","PeriodicalId":340802,"journal":{"name":"New Spaces in Mathematics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126145802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Topology and Algebraic Topology","authors":"","doi":"10.1017/9781108854429.006","DOIUrl":"https://doi.org/10.1017/9781108854429.006","url":null,"abstract":"","PeriodicalId":340802,"journal":{"name":"New Spaces in Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125568583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Topo-logie","authors":"Mathieu Anel, A. Joyal","doi":"10.1017/9781108854429.007","DOIUrl":"https://doi.org/10.1017/9781108854429.007","url":null,"abstract":"","PeriodicalId":340802,"journal":{"name":"New Spaces in Mathematics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125250592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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