Eilenberg–Maclane空间与同构型理论中的稳定

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2023-09-21 DOI:10.1007/s40062-023-00330-5

David Wärn

{"title":"Eilenberg–Maclane空间与同构型理论中的稳定","authors":"David Wärn","doi":"10.1007/s40062-023-00330-5","DOIUrl":null,"url":null,"abstract":"<div><p>In this note, we study the delooping of spaces and maps in homotopy type theory. We show that in some cases, spaces have a unique delooping, and give a simple description of the delooping in these cases. We explain why some maps, such as group homomorphisms, have a unique delooping. We discuss some applications to Eilenberg–MacLane spaces and cohomology.</p></div>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"18 2-3","pages":"357 - 368"},"PeriodicalIF":0.5000,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40062-023-00330-5.pdf","citationCount":"1","resultStr":"{\"title\":\"Eilenberg–Maclane spaces and stabilisation in homotopy type theory\",\"authors\":\"David Wärn\",\"doi\":\"10.1007/s40062-023-00330-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this note, we study the delooping of spaces and maps in homotopy type theory. We show that in some cases, spaces have a unique delooping, and give a simple description of the delooping in these cases. We explain why some maps, such as group homomorphisms, have a unique delooping. We discuss some applications to Eilenberg–MacLane spaces and cohomology.</p></div>\",\"PeriodicalId\":636,\"journal\":{\"name\":\"Journal of Homotopy and Related Structures\",\"volume\":\"18 2-3\",\"pages\":\"357 - 368\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-09-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s40062-023-00330-5.pdf\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Homotopy and Related Structures\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40062-023-00330-5\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Homotopy and Related Structures","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40062-023-00330-5","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 1

摘要

在这篇文章中，我们研究了空间和映射在同伦型理论中的离域问题。我们证明了在某些情况下，空间有一个独特的离域，并给出了这些情况下离域的简单描述。我们解释了为什么一些映射，比如群同态，有一个独特的离域。我们讨论了Eilenberg–MacLane空间和上同调的一些应用。

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

Eilenberg–Maclane spaces and stabilisation in homotopy type theory

In this note, we study the delooping of spaces and maps in homotopy type theory. We show that in some cases, spaces have a unique delooping, and give a simple description of the delooping in these cases. We explain why some maps, such as group homomorphisms, have a unique delooping. We discuss some applications to Eilenberg–MacLane spaces and cohomology.

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

Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

自引率

0.00%

发文量

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.