{"title":"合成$infty$类之间的可扩函数","authors":"César Bardomiano-Martínez","doi":"arxiv-2407.18072","DOIUrl":null,"url":null,"abstract":"We study exponentiable functors in the context of synthetic\n$\\infty$-categories. We do this within the framework of simplicial Homotopy\nType Theory of Riehl and Shulman. Our main result characterizes exponentiable\nfunctors. In order to achieve this, we explore Segal type completions.\nMoreover, we verify that our result is semantically sound.","PeriodicalId":501135,"journal":{"name":"arXiv - MATH - Category Theory","volume":"350 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Exponentiable functors between synthetic $\\\\infty$-categories\",\"authors\":\"César Bardomiano-Martínez\",\"doi\":\"arxiv-2407.18072\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study exponentiable functors in the context of synthetic\\n$\\\\infty$-categories. We do this within the framework of simplicial Homotopy\\nType Theory of Riehl and Shulman. Our main result characterizes exponentiable\\nfunctors. In order to achieve this, we explore Segal type completions.\\nMoreover, we verify that our result is semantically sound.\",\"PeriodicalId\":501135,\"journal\":{\"name\":\"arXiv - MATH - Category Theory\",\"volume\":\"350 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-25\",\"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-2407.18072\",\"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-2407.18072","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Exponentiable functors between synthetic $\infty$-categories
We study exponentiable functors in the context of synthetic
$\infty$-categories. We do this within the framework of simplicial Homotopy
Type Theory of Riehl and Shulman. Our main result characterizes exponentiable
functors. In order to achieve this, we explore Segal type completions.
Moreover, we verify that our result is semantically sound.
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