Intrinsic Schreier Split Extensions

  • Andrea Montoli
  • Diana RodeloEmail author
  • Tim Van der Linden


In the context of regular unital categories we introduce an intrinsic version of the notion of a Schreier split epimorphism, originally considered for monoids. We show that such split epimorphisms satisfy the same homological properties as Schreier split epimorphisms of monoids do. This gives rise to new examples of \({\mathcal {S}}\)-protomodular categories, and allows us to better understand the homological behaviour of monoids from a categorical perspective.


Fibration of points Jointly extremal-epimorphic pair Regular category Unital category Protomodular category Monoid Jónsson–Tarski variety 

Mathematics Subject Classification

20M32 20J15 18E99 03C05 08C05 



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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Dipartimento di Matematica “Federigo Enriques”Università degli Studi di MilanoMilanoItaly
  2. 2.Departamento de Matemática, Faculdade de Ciências e TecnologiaUniversidade do AlgarveFaroPortugal
  3. 3.CMUC, Department of MathematicsUniversity of CoimbraCoimbraPortugal
  4. 4.Institut de Recherche en Mathématique et PhysiqueUniversité catholique de LouvainLouvain-la-NeuveBelgium

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