@article{article_524459, title={Hom-coalgebra cleft extensions and braided tensor Hom-categories of Hom-entwining structures}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={48}, pages={186–199}, year={2019}, author={Quanguo, Chen and Dingguo, Wang}, keywords={Hom-Hopf algebra,Hom-entwining structure,cleft extension}, abstract={We investigate how the category of Hom-entwined modules can be made into a monoidal category. The sufficient and necessary conditions making the category of Hom-entwined modules have a braiding are given. Also, we formulate the concept of Hom-cleft extension for a Hom-entwining structure, and prove that if $(A, \alpha)$ is a $(C,\gamma)$-cleft extension, then there is an isomorphism of Hom-algebras between $(A, \alpha)$ and  a crossed product Hom-algebra of $A^{coC}$ and $C$. <br>}, number={1}, publisher={Hacettepe University}