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.
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|Titolo:||A good theory of ideals in regular multi-pointed categories|
|Citazione:||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.|
|Appare nelle tipologie:||1.1 Articolo in rivista|