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Construction of Braided Monoidal Category over a Coring
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SHEN Bingliang1，LIU Ling2
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(1. Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China； 2. College of
Mathematics, Physics & Information Engineering, Zhejiang Normal University, Jinhua 321004, China)
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Abstract The purpose of this paper is to investigate how the category of the comodules of the coring can be made into a braided monoidal category. Firstly, the conditions making the category into a monoidal category are obtained by using the fact that if C is a coring, then C can be made into a Ccomodule. The conditions are that the algebra and coring in question are bialgebra and biring,with some extra compatibility relations. Then, given a monodial category of comodules of the coring, the braiding is constructed by means of a twisted convolution invertible map and the sufficient and necessary conditions making the category form into a braided monoidal category are obtained. The category of entwined modules is contained in the category of the comodules of the coring. Lastly, the construction can be applied to the category of entwined modules as an example.
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Received: 29 January 2010
Published: 31 December 2010
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