Relation between Ann-categories and ring categories

Che Thi Kim Phung; Nguyen Tien Quang; Nguyen Thu Thuy

doi:10.4134/CKMS.2010.25.4.523

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2010; 25(4): 523-535

Printed December 1, 2010

https://doi.org/10.4134/CKMS.2010.25.4.523

Relation between Ann-categories and ring categories

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

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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

MSC numbers: 18D10