The Nine Lemma and the push forward construction for special Schreier extensions of monoids with operations
- 47 Downloads
We show that the Nine Lemma holds for special Schreier extensions of monoids with operations. This fact is used to obtain a push forward construction for special Schreier extensions with abelian kernel. This construction permits to give a functorial description of the Baer sum of such extensions.
KeywordsMonoids with operations Special Schreier extension Nine Lemma Push forward Baer sum
We wish to express our gratitude to Alex Patchkoria for pointing out to us the existence of some old literature, of not easy access, related to the subject of this paper. This work was partially supported by the Centre for Mathematics of the University of Coimbra – UID/MAT/00324/2013, by ESTG and CDRSP from the Polytechnical Institute of Leiria – UID/Multi/04044/2013, funded by the Portuguese Government through FCT/MCTES and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020. This work was partially supported by the Programma per Giovani Ricercatori “Rita Levi-Montalcini”, Funded by the Italian government through MIUR.
- 1.Barr, M.: Exact Categories, Lecture Notes in Mathematics, vol. 236, pp. 1–120. Springer, Berlin (1971)Google Scholar
- 2.Bourn, D., Martins-Ferreira, N., Montoli, A., Sobral, M.: Schreier split epimorphisms in monoids and in semirings, Textos de Matemática (Série B), Departamento de Matemática da Universidade de Coimbra, vol. 45 (2013)Google Scholar
- 9.Mal’cev, A.I.: On the general theory of algebraic systems. Mat. Sbornik N.S. 35, 3–20 (1954)Google Scholar
- 15.Patchkoria, A.: Extensions of semimodules by monoids and their cohomological characterization. Bull. Georgian Acad. Sci. 86, 21–24 (1977)Google Scholar