{"title":"Functors for Long dimodules and Yetter–Drinfeld modules in a weak setting","authors":"J. Álvarez, R. G. Rodríguez","doi":"10.4171/rsmup/125","DOIUrl":null,"url":null,"abstract":"In this paper, for two weak Hopf monoids H and B with invertible antipode, we define a functor between the category of left-leftH⊗B-Yetter-Drinfeld modules and the one of H-B-Long dimodules. We also show that, if moreover H is quasitriangular and B is coquasitriangular, this functor is a retraction of the well-known injective functor between left-left H-B-Long dimodules and left-left H ⊗B-Yetter-Drinfeld modules. Mathematics Subject Classification (2020). Primary: 16T05; Secondary: 18M05, 18M15, 16T25.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"560 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rendiconti del Seminario Matematico della Università di Padova","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/rsmup/125","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 paper, for two weak Hopf monoids H and B with invertible antipode, we define a functor between the category of left-leftH⊗B-Yetter-Drinfeld modules and the one of H-B-Long dimodules. We also show that, if moreover H is quasitriangular and B is coquasitriangular, this functor is a retraction of the well-known injective functor between left-left H-B-Long dimodules and left-left H ⊗B-Yetter-Drinfeld modules. Mathematics Subject Classification (2020). Primary: 16T05; Secondary: 18M05, 18M15, 16T25.
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