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Quasi-bimonads and their representations
Authors:Xiaohui Zhang  Xiaofan Zhao  Wei Wang
Affiliation:1. School of Mathematical Sciences, Qufu Normal University, Qufu Shandong 273165, PR China;2. College of Mathematics and Information Science, Henan Normal University, Xinxiang Henan 453007, PR China;3. Nanjing Research Institute of Electronic Engineering, Nanjing Jiangsu 210007, PR China;1. Departamento de Matemática, Universidade Estadual de Maringá, Avenida Colombo, 5790, 87020-900, Maringá, PR, Brazil;2. Instituto de Matemática, Universidade Federal do Rio Grande do Sul, 91509-900, Porto Alegre, RS, Brazil;1. University of Bucharest, Faculty of Mathematics and Computer Science, Str. Academiei 14, Bucharest 1, RO-010014, Romania;2. Institute of Mathematics of the Romanian Academy, PO-Box 1-764 RO-014700, Bucharest, Romania;1. Wayne State University, Detroit, MI 48202, USA;2. Eurasian National University, Astana, Kazakhstan;3. FES-Cuautitlán, UNAM, Campo 1, Mexico
Abstract:
In this paper quasi-bimonads on a monoidal category are introduced and investigated. Quasi-bimonads generalize quasi-bialgebras to a non-braided setting. We discuss their representations and investigate the R-matrix of a quasi-bimonad. Such an R-matrix provides a new solution of the version of the Yang-Baxter equation adapted to the situation. We also introduce an equivalent relation on (quasitriangular) quasi-bimonads such that the categories of representations of two (quasitriangular) quasi-bimonads are (braided) monoidal equivalent. Finally, we discuss Drinfeld twists and Hom quasi-bialgebras.
Keywords:Quasi-bimonad  Bimonad  Gauge transformation  Hom-bialgebra
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