{"title":"Cyclic Segal Spaces","authors":"Julia E. Bergner, Walker H. Stern","doi":"arxiv-2409.11945","DOIUrl":null,"url":null,"abstract":"In this survey article, we review some conceptual approaches to the cyclic\ncategory $\\Lambda$, as well as its description as a crossed simplicial group.\nWe then give a new proof of the model structure on cyclic sets, work through\nthe details of the generalized Reedy structure on cyclic spaces, and introduce\nmodel structures for cyclic Segal spaces and cyclic 2-Segal spaces.","PeriodicalId":501135,"journal":{"name":"arXiv - MATH - Category Theory","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","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-2409.11945","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this survey article, we review some conceptual approaches to the cyclic
category $\Lambda$, as well as its description as a crossed simplicial group.
We then give a new proof of the model structure on cyclic sets, work through
the details of the generalized Reedy structure on cyclic spaces, and introduce
model structures for cyclic Segal spaces and cyclic 2-Segal spaces.