Martins-Ferreira, NelsonMontoli, AndreaSobral, Manuela2023-05-262023-05-262018-08-10Martins-Ferreira, N., Montoli, A. & Sobral, M. The Nine Lemma and the push forward construction for special Schreier extensions of monoids with operations. Semigroup Forum 97, 325–352 (2018). https://doi.org/10.1007/s00233-018-9962-11432-2137http://hdl.handle.net/10400.8/8523Acknowledgements: 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.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.engMonoids with operationsSpecial Schreier extensionNine LemmaPush forwardBaer sumjournal articlehttps://doi.org/10.1007/s00233-018-9962-1