{"title":"通过三角范畴的重归纳,构建理想的共轭对","authors":"Qikai Wang, Haiyan Zhu","doi":"arxiv-2406.00417","DOIUrl":null,"url":null,"abstract":"Let $(\\mathcal{T}',\\mathcal{T},\\mathcal{T}'')$ be a recollement of\ntriangulated categories. Two complete ideal cotorsion pairs in $\\mathcal{T}'$\nand $\\mathcal{T}''$ can be induced by a complete ideal cotorsion pair in\n$\\mathcal{T}$. If $(\\mathcal{I},\\mathcal{I}^\\perp )$ and\n$(\\mathcal{J},\\mathcal{J}^\\perp)$ are two complete ideal cotorsion pair in\ntriangulated category, then\n$(\\mathcal{I}\\cap\\mathcal{J},\\langle\\mathcal{I}^\\perp,\\mathcal{J}^\\perp\\rangle)$\nis also a complete ideal cotorsion pair. In this way, a series of ideal\ncotorsion pairs in $\\mathcal{T}$ can be induced by two ideal cotorsion pairs in\n$\\mathcal{T}'$ and $\\mathcal{T}''$.","PeriodicalId":501135,"journal":{"name":"arXiv - MATH - Category Theory","volume":"14 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Construct ideal cotorsion pairs by recollement of triangulated categories\",\"authors\":\"Qikai Wang, Haiyan Zhu\",\"doi\":\"arxiv-2406.00417\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $(\\\\mathcal{T}',\\\\mathcal{T},\\\\mathcal{T}'')$ be a recollement of\\ntriangulated categories. Two complete ideal cotorsion pairs in $\\\\mathcal{T}'$\\nand $\\\\mathcal{T}''$ can be induced by a complete ideal cotorsion pair in\\n$\\\\mathcal{T}$. If $(\\\\mathcal{I},\\\\mathcal{I}^\\\\perp )$ and\\n$(\\\\mathcal{J},\\\\mathcal{J}^\\\\perp)$ are two complete ideal cotorsion pair in\\ntriangulated category, then\\n$(\\\\mathcal{I}\\\\cap\\\\mathcal{J},\\\\langle\\\\mathcal{I}^\\\\perp,\\\\mathcal{J}^\\\\perp\\\\rangle)$\\nis also a complete ideal cotorsion pair. In this way, a series of ideal\\ncotorsion pairs in $\\\\mathcal{T}$ can be induced by two ideal cotorsion pairs in\\n$\\\\mathcal{T}'$ and $\\\\mathcal{T}''$.\",\"PeriodicalId\":501135,\"journal\":{\"name\":\"arXiv - MATH - Category Theory\",\"volume\":\"14 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-06-01\",\"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-2406.00417\",\"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-2406.00417","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Construct ideal cotorsion pairs by recollement of triangulated categories
Let $(\mathcal{T}',\mathcal{T},\mathcal{T}'')$ be a recollement of
triangulated categories. Two complete ideal cotorsion pairs in $\mathcal{T}'$
and $\mathcal{T}''$ can be induced by a complete ideal cotorsion pair in
$\mathcal{T}$. If $(\mathcal{I},\mathcal{I}^\perp )$ and
$(\mathcal{J},\mathcal{J}^\perp)$ are two complete ideal cotorsion pair in
triangulated category, then
$(\mathcal{I}\cap\mathcal{J},\langle\mathcal{I}^\perp,\mathcal{J}^\perp\rangle)$
is also a complete ideal cotorsion pair. In this way, a series of ideal
cotorsion pairs in $\mathcal{T}$ can be induced by two ideal cotorsion pairs in
$\mathcal{T}'$ and $\mathcal{T}''$.