Che Thi Kim Phung, Nguyen Tien Quang, and Nguyen Thu Thuy 783 Pham Huu Lau Street,Cao Lanh City, Hanoi National University of Education, Hanoi National University of Education
Abstract : There are different categorifications of the notion of a $ring$ such as $Ann$-$category$ due to N. T. Quang, $ring$ $category$ due to M. M. Kapranov and V. A. Voevodsky. The main result of this paper is to prove that every axiom in the definition of a $ring$ $category$, but the axiom $x_{0}=y_{0},$ can be deduced from the axiomatics of an $Ann$-$category$.
Keywords : Ann-category, ring category, distributivity constraint
