RELATION BETWEEN ANN-CATEGORIES AND RING CATEGORIES
Che Thi Kim Phung, Nguyễn Tiến Quang, Nguyen Thu Thuy · Communications of the Korean Mathematical Society · 2010
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.