弱分配律的凸性

Log. Methods Comput. Sci. Pub Date : 2021-08-19 DOI:10.46298/lmcs-18(4:8)2022

F. Bonchi, A. Santamaria

{"title":"弱分配律的凸性","authors":"F. Bonchi, A. Santamaria","doi":"10.46298/lmcs-18(4:8)2022","DOIUrl":null,"url":null,"abstract":"We study the canonical weak distributive law $\\delta$ of the powerset monad\nover the semimodule monad for a certain class of semirings containing, in\nparticular, positive semifields. For this subclass we characterise $\\delta$ as\na convex closure in the free semimodule of a set. Using the abstract theory of\nweak distributive laws, we compose the powerset and the semimodule monads via\n$\\delta$, obtaining the monad of convex subsets of the free semimodule.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"16 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Convexity via Weak Distributive Laws\",\"authors\":\"F. Bonchi, A. Santamaria\",\"doi\":\"10.46298/lmcs-18(4:8)2022\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the canonical weak distributive law $\\\\delta$ of the powerset monad\\nover the semimodule monad for a certain class of semirings containing, in\\nparticular, positive semifields. For this subclass we characterise $\\\\delta$ as\\na convex closure in the free semimodule of a set. Using the abstract theory of\\nweak distributive laws, we compose the powerset and the semimodule monads via\\n$\\\\delta$, obtaining the monad of convex subsets of the free semimodule.\",\"PeriodicalId\":314387,\"journal\":{\"name\":\"Log. Methods Comput. Sci.\",\"volume\":\"16 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-08-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Log. Methods Comput. Sci.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46298/lmcs-18(4:8)2022\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Log. Methods Comput. Sci.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/lmcs-18(4:8)2022","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

研究了一类包含正半域的半环在半模单上幂集单的正则弱分配律。对于这个子类，我们在集合的自由半模中将$\delta$描述为凸闭包。利用弱分配律的抽象理论，通过$\ δ $组合幂集和半模单，得到了自由半模凸子集的单。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Convexity via Weak Distributive Laws

We study the canonical weak distributive law $\delta$ of the powerset monad over the semimodule monad for a certain class of semirings containing, in particular, positive semifields. For this subclass we characterise $\delta$ as a convex closure in the free semimodule of a set. Using the abstract theory of weak distributive laws, we compose the powerset and the semimodule monads via $\delta$, obtaining the monad of convex subsets of the free semimodule.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Log. Methods Comput. Sci.

自引率

0.00%

发文量