Subtractive Categories and Extended Subtractions |
| |
Authors: | Dominique Bourn Zurab Janelidze |
| |
Institution: | (1) Laboratoire de Mathématiques Pures et Appliquées, Université du Littoral, Bat. H. Poincaré, 50 Rue F. Buisson, BP 699, 62228 Calais, France;(2) Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, Cape Town, South Africa |
| |
Abstract: | We introduce a notion of an extended operation which should serve as a new tool for the study of categories like Mal’tsev, unital, strongly unital and subtractive categories.
However, in the present paper we are only concerned with subtractive categories, and accordingly, most of the time we will
deal with extended subtractions, which are particular instances of extended operations. We show that these extended subtractions provide new conceptual characterizations
of subtractive categories and moreover, they give an enlarged “algebraic tool” for working in a subtractive category—we demonstrate
this by using them to describe the construction of associated abelian objects in regular subtractive categories with finite colimits. Also, the definition and some basic properties of abelian objects
in a general subtractive category is given for the first time in the present paper.
The second author acknowledges the support of Claude Leon Foundation, INTAS (06-1000017-8609) and Georgian National Science
Foundation (GNSF/ST06/3-004). |
| |
Keywords: | Mal’ tsev category Unital category Strongly unital category Subtractive category Abelian objects Natural operations |
本文献已被 SpringerLink 等数据库收录! |
|