中文摘要：

讨论了Turaev π-代数余模范畴中的pivotal群交叉结构和ribbon群交叉结构,引入余pivotal Turaev π-代数和余ribbon Turaev π-代数的定义,并分别给出Turaev π-代数伴有余pivotal结构和余ribon结构的充要条件.

英文摘要：

The crossed ribbon structure and crossed pivotal structure in Corep（H）are studied,where the category of π-comodules over a Turaev π-algebra H.The notions of a copivotal Turaevπ-algebra and a coribbon Turaev π-algebra are introduced.Finally,the necessary and sufficient conditions for Corep（H）to be a crossed pivotal category and to be a crossed ribbon category are given.