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On the categorical behaviour of preordered groups
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Advisor(s)
Abstract(s)
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.
Description
The authors are grateful to George Janelidze for fruitful discussions on the topic of the present paper, and to the referee for several suggestions that helped to improve the final version of the paper.
The first author was partially supported by Centro de Matemática da Universidade de Coimbra – UID/MAT/00324/2013, funded by the Portuguese Government through FCT/MCTES and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020, and by the FCT Sabbatical Grant SFRH/BSAB/127925/2016. The second author was partially supported by the Fundação para a Ciência e a Tecnologia (FCT) and Centro2020 through the Project references: UID/Multi/04044/2013 and PAMI – ROTEIRO/0328/2013 (N.022158).
The third author was partially supported by the Programma per Giovani Ricercatori “Rita Levi-Montalcini”, funded by the Italian government through MIUR.
Keywords
Preordered group Positive cone Protomodular object S-Protomodular category
Citation
Clementino, Maria & Martins-Ferreira, Nelson & Montoli, Andrea. (2019). On the categorical behaviour of preordered groups. Journal of Pure and Applied Algebra. 223:10. https://doi.org/10.1016/j.jpaa.2019.01.006
Publisher
Elsevier - ScienceDirect