We study the categorical properties of preordered groups. We first give a description of limits and colimits in this category, and study some classical exactness properties. Then we point out a strong analogy between the algebraic behaviour of preordered groups and monoids, and we apply two different recent approaches to relative categorical algebra to obtain some homological properties of preordered groups.
On the categorical behaviour of preordered groups / M.M. Clementino, N. Martins-Ferreira, A. Montoli. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 223:10(2019 Oct), pp. 4226-4245. [10.1016/j.jpaa.2019.01.006]
On the categorical behaviour of preordered groups
A. Montoli
Ultimo
2019
Abstract
We study the categorical properties of preordered groups. We first give a description of limits and colimits in this category, and study some classical exactness properties. Then we point out a strong analogy between the algebraic behaviour of preordered groups and monoids, and we apply two different recent approaches to relative categorical algebra to obtain some homological properties of preordered groups.
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