TITLE:
The Integrals of Entwining Structure
AUTHORS:
Yuzhuo Yuan, Lihong Dong, Zhengming Jiao
KEYWORDS:
Entwining Structure; Integral; Forgetful Functor; Natural Transformation
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.3 No.4,
July
1,
2013
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.