{"title":"通过项链丰富类别的神经","authors":"Arne Mertens","doi":"arxiv-2408.10049","DOIUrl":null,"url":null,"abstract":"We introduce necklicial nerve functors from enriched categories to simplicial\nsets, which include Cordier's homotopy coherent, Lurie's differential graded\nand Le Grignou's cubical nerves. It is shown that every necklicial nerve can be\nlifted to the templicial objects of arXiv:2302.02484v2. Building on the work of\nDugger and Spivak, we give sufficient conditions under which the left-adjoint\nof a necklicial nerve can be described more explicitly. As an application, we\nobtain novel and simple expressions for the left-adjoints of the dg-nerve and\ncubical nerve.","PeriodicalId":501135,"journal":{"name":"arXiv - MATH - Category Theory","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Nerves of enriched categories via necklaces\",\"authors\":\"Arne Mertens\",\"doi\":\"arxiv-2408.10049\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce necklicial nerve functors from enriched categories to simplicial\\nsets, which include Cordier's homotopy coherent, Lurie's differential graded\\nand Le Grignou's cubical nerves. It is shown that every necklicial nerve can be\\nlifted to the templicial objects of arXiv:2302.02484v2. Building on the work of\\nDugger and Spivak, we give sufficient conditions under which the left-adjoint\\nof a necklicial nerve can be described more explicitly. As an application, we\\nobtain novel and simple expressions for the left-adjoints of the dg-nerve and\\ncubical nerve.\",\"PeriodicalId\":501135,\"journal\":{\"name\":\"arXiv - MATH - Category Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-19\",\"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-2408.10049\",\"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-2408.10049","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We introduce necklicial nerve functors from enriched categories to simplicial
sets, which include Cordier's homotopy coherent, Lurie's differential graded
and Le Grignou's cubical nerves. It is shown that every necklicial nerve can be
lifted to the templicial objects of arXiv:2302.02484v2. Building on the work of
Dugger and Spivak, we give sufficient conditions under which the left-adjoint
of a necklicial nerve can be described more explicitly. As an application, we
obtain novel and simple expressions for the left-adjoints of the dg-nerve and
cubical nerve.