{"title":"一般组合模型范畴中经由同伦末端的同伦极限","authors":"Sergey Arkhipov, Sebastian Ørsted","doi":"10.1007/s10485-023-09747-8","DOIUrl":null,"url":null,"abstract":"<div><p>We prove and explain several classical formulae for homotopy (co)limits in general (combinatorial) model categories which are not necessarily simplicially enriched. Importantly, we prove versions of the Bousfield–Kan formula and the fat totalization formula in this complete generality. We finish with a proof that homotopy-final functors preserve homotopy limits, again in complete generality.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Homotopy (Co)limits via Homotopy (Co)ends in General Combinatorial Model Categories\",\"authors\":\"Sergey Arkhipov, Sebastian Ørsted\",\"doi\":\"10.1007/s10485-023-09747-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove and explain several classical formulae for homotopy (co)limits in general (combinatorial) model categories which are not necessarily simplicially enriched. Importantly, we prove versions of the Bousfield–Kan formula and the fat totalization formula in this complete generality. We finish with a proof that homotopy-final functors preserve homotopy limits, again in complete generality.</p></div>\",\"PeriodicalId\":7952,\"journal\":{\"name\":\"Applied Categorical Structures\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-11-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Categorical Structures\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10485-023-09747-8\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Categorical Structures","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10485-023-09747-8","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Homotopy (Co)limits via Homotopy (Co)ends in General Combinatorial Model Categories
We prove and explain several classical formulae for homotopy (co)limits in general (combinatorial) model categories which are not necessarily simplicially enriched. Importantly, we prove versions of the Bousfield–Kan formula and the fat totalization formula in this complete generality. We finish with a proof that homotopy-final functors preserve homotopy limits, again in complete generality.
期刊介绍：
Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, physics and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorification of (geometric) invariants, categorical investigations in mathematical physics, higher category theory and applications, categorical investigations in functional analysis, in continuous order theory and in theoretical computer science. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant.
Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
