We extend the notion of an ‘‘ideal’’ from regular pointed categories to regular multi-pointed categories, and having ‘‘a good theory of ideals’’ will mean that there is a bijection between ideals and kernel pairs, which in the pointed case is the main property of ideal determined categories. The study of general categories with a good theory of ideals allows in fact a simultaneous treatment of ideal determined and Barr exact Goursat categories:weprove that in the case when all morphisms are chosen as null morphisms, the presence of a good theory of ideals becomes precisely the property for a regular category to be a Barr exact Goursat category.

Janelidze, Z., Gran, M., Ursini, A. (2012). A good theory of ideals in regular multi-pointed categories. JOURNAL OF PURE AND APPLIED ALGEBRA, 216, 1905-1919 [10.1016/j.jpaa.2012.02.028].

A good theory of ideals in regular multi-pointed categories

URSINI, ALDO
2012-01-01

Abstract

We extend the notion of an ‘‘ideal’’ from regular pointed categories to regular multi-pointed categories, and having ‘‘a good theory of ideals’’ will mean that there is a bijection between ideals and kernel pairs, which in the pointed case is the main property of ideal determined categories. The study of general categories with a good theory of ideals allows in fact a simultaneous treatment of ideal determined and Barr exact Goursat categories:weprove that in the case when all morphisms are chosen as null morphisms, the presence of a good theory of ideals becomes precisely the property for a regular category to be a Barr exact Goursat category.
2012
Janelidze, Z., Gran, M., Ursini, A. (2012). A good theory of ideals in regular multi-pointed categories. JOURNAL OF PURE AND APPLIED ALGEBRA, 216, 1905-1919 [10.1016/j.jpaa.2012.02.028].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/443613
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