The Integrals of Entwining Structure

Yuzhuo Yuan, Lihong Dong, Zhengming Jiao

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1Department of Mathematics, Henan Normal University, Xinxiang, China 2Department of Mathematics, Nanyang Normal University, Nanyang, China.

DOI: 10.4236/apm.2013.34055                

Abstract

In this paper the integrals of entwining structure (A,C,ψ) are discussed, where A is a k-algebra, C a k-coalgebra and a k-linear map. We prove that there exists a normalized integral γ:C→Hom(C,A) of (A,C,ψ) if and only if any representation of (A,C,ψ) is injective in a functorial way as a corepresentation of C. We give the dual results as well.

Keywords

Entwining Structure; Integral; Forgetful Functor; Natural Transformation

Conflicts of Interest

The authors declare no conflicts of interest.

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