有理π-分次模与π-余模在有理对上的范畴同构

CATEGORY OF ALL RATIONAL Π-GRADED MODULES IS ISOMORPHIC TO THE CATEGORY OF ALL Π-COMODULES ON RATIONAL PAIRINGS

设A=( )α∈πAα为丌-分次代数,C={Cα}α∈π为丌-余代数,本文证明了(1)(C,A,〈-,-〉)为有理对时,RatC(AM)≌MC;(2)丌为有限群时,(C,A,〈-,-〉)为有理对当且仅当存在单余代数同态:( )α∈πCα→A0.