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The Integrals of Entwining Structure
1Department of Mathematics, Henan Normal University, Xinxiang, China 2Department of Mathematics, Nanyang Normal University, Nanyang, China
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- 3 1Department of Mathematics, Henan Normal University, Xinxiang, China 2Department of Mathematics, Nanyang Normal University, Nanyang, China
Advances in Pure Mathematics·Volume 03 (2013)·Pages 381–389·Published 1 July 2013·DOI10.4236/apm.2013.34055
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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.
KeywordsEntwining StructureIntegralForgetful FunctorNatural Transformation
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