拓扑空间和开放映射范畴没有乘积

arXiv - MATH - Category Theory Pub Date : 2024-07-19 DOI:arxiv-2407.13951

Guram Bezhanishvili, Andre Kornell

{"title":"拓扑空间和开放映射范畴没有乘积","authors":"Guram Bezhanishvili, Andre Kornell","doi":"arxiv-2407.13951","DOIUrl":null,"url":null,"abstract":"We prove that the category of topological spaces and open maps does not have\nbinary products, thus resolving the Esakia-Janelidze problem in the negative.\nWe also prove that the categories of complete Heyting algebras and complete\nclosure algebras do not have binary coproducts.","PeriodicalId":501135,"journal":{"name":"arXiv - MATH - Category Theory","volume":"11 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The category of topological spaces and open maps does not have products\",\"authors\":\"Guram Bezhanishvili, Andre Kornell\",\"doi\":\"arxiv-2407.13951\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that the category of topological spaces and open maps does not have\\nbinary products, thus resolving the Esakia-Janelidze problem in the negative.\\nWe also prove that the categories of complete Heyting algebras and complete\\nclosure algebras do not have binary coproducts.\",\"PeriodicalId\":501135,\"journal\":{\"name\":\"arXiv - MATH - Category Theory\",\"volume\":\"11 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Category Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2407.13951\",\"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 - Category Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.13951","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

我们证明了拓扑空间和开映射范畴不存在二元乘积，从而从反面解决了埃萨基亚-詹利泽问题。我们还证明了完全海廷代数和完全闭合代数范畴不存在二元共乘积。

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

The category of topological spaces and open maps does not have products

We prove that the category of topological spaces and open maps does not have binary products, thus resolving the Esakia-Janelidze problem in the negative. We also prove that the categories of complete Heyting algebras and complete closure algebras do not have binary coproducts.

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

arXiv - MATH - Category Theory

自引率

0.00%

发文量