Cat弱Hopf代数

摘要

首先引入pre-cat弱Hopf代数和cat弱Hopf代数来刻画具有投射的弱Hopf代数的性质,并建立pre-cat弱Hopf代数的张量范畴,证明了pre-cat弱Hopf代数是cat弱Hopf代数的充要条件,从而推广了LODAY引入的cat-群和cat Hopf代数的相应结论.%In this paper, we first introduce the notions of pre-cat weak Hopf algebras and cat weak Hopf algebras to characterize the structures of weak Hopf algebras with projections.Then, we give the monoidal category of these objects which generalize the results of cat Hopf algebras and cat-groups introduced by LODAY.