{"title":"收敛和富量子范畴","authors":"Dirk Hofmann, C. Reis","doi":"10.29252/CGASA.9.1.77","DOIUrl":null,"url":null,"abstract":"Generalising Nachbin's theory of \"topology and order\", in this paper we continue the study of quantale-enriched categories equipped with a compact Hausdorff topology. We compare these $\\mathcal{V}$-categorical compact Hausdorff spaces with ultrafilter-quantale-enriched categories, and show that the presence of a compact Hausdorff topology guarantees Cauchy completeness and (suitably defined) codirected completeness of the underlying quantale enriched category.","PeriodicalId":170235,"journal":{"name":"Categories and General Algebraic Structures with Application","volume":"108 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Convergence and quantale-enriched categories\",\"authors\":\"Dirk Hofmann, C. Reis\",\"doi\":\"10.29252/CGASA.9.1.77\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Generalising Nachbin's theory of \\\"topology and order\\\", in this paper we continue the study of quantale-enriched categories equipped with a compact Hausdorff topology. We compare these $\\\\mathcal{V}$-categorical compact Hausdorff spaces with ultrafilter-quantale-enriched categories, and show that the presence of a compact Hausdorff topology guarantees Cauchy completeness and (suitably defined) codirected completeness of the underlying quantale enriched category.\",\"PeriodicalId\":170235,\"journal\":{\"name\":\"Categories and General Algebraic Structures with Application\",\"volume\":\"108 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-05-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Categories and General Algebraic Structures with Application\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.29252/CGASA.9.1.77\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Categories and General Algebraic Structures with Application","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.29252/CGASA.9.1.77","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Generalising Nachbin's theory of "topology and order", in this paper we continue the study of quantale-enriched categories equipped with a compact Hausdorff topology. We compare these $\mathcal{V}$-categorical compact Hausdorff spaces with ultrafilter-quantale-enriched categories, and show that the presence of a compact Hausdorff topology guarantees Cauchy completeness and (suitably defined) codirected completeness of the underlying quantale enriched category.
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