余拟三角弱Hopf群代数与辫子Monoidal范畴

In this paper, we first give the definitions of a crossed left π-H-comodules over a crossed weak Hopf π-algebra H, and show that the category of crossed left π-H-comodules is a monoidal category. Finally, we show that a family σ = {σα,β: Hα Hβ→ k}α,β∈πof k-linear maps is a coquasitriangular structure of a crossed weak Hopf π-algebra H if and only if the category of crossed left π-H-comodules over H is a braided monoidal category with braiding defined by σ.

Coquasitriangular Weak Hopf Group Algebras and Braided Monoidal Categories

In this paper, we first give the definitions of a crossed left $\pi$-$H$-comodules over a crossed weak Hopf $\pi$-algebra $H$, and show that the category of crossed left $\pi$-$H$-comodules is a monoidal category. Finally, we show that a family $\sigma=\{\sigma_{\a,\b}: H_{\a}\o H_{\b}\rightarrow k\}_{\a,\b\in \pi}$ of $k$-linear maps is a coquasitriangular structure of a crossed weak Hopf $\pi$-algebra $H$ if and only if the category of crossed left $\pi$-$H$-comodules over $H$ is a braided monoidal category with braiding defined by $\sigma$.