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Intrinsic Schreier Split Extensions

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Abstract

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.

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Authors and Affiliations

  1. Dipartimento di Matematica “Federigo Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133, Milano, Italy

    Andrea Montoli

  2. Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade do Algarve, Campus de Gambelas, 8005-139, Faro, Portugal

    Diana Rodelo

  3. CMUC, Department of Mathematics, University of Coimbra, 3001-501, Coimbra, Portugal

    Diana Rodelo

  4. Institut de Recherche en Mathématique et Physique, Université catholique de Louvain, chemin du cyclotron 2 bte L7.01.02, 1348, Louvain-la-Neuve, Belgium

    Tim Van der Linden

Authors
  1. Andrea Montoli
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  2. Diana Rodelo
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  3. Tim Van der Linden
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Corresponding author

Correspondence to Diana Rodelo.

Additional information

Communicated by M.M. Clementino.

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Andrea Montoli was partially supported by the Programma per Giovani Ricercatori “Rita Levi-Montalcini”, funded by the Italian government through MIUR.

Diana Rodelo acknowledges partial financial assistance by the Centre for Mathematics of the University of Coimbra—UID/MAT/00324/2019, funded by the Portuguese Government through FCT/MEC and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020.

Tim Van der Linden is a Research Associate of the Fonds de la Recherche Scientifique–FNRS.

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Montoli, A., Rodelo, D. & Van der Linden, T. Intrinsic Schreier Split Extensions. Appl Categor Struct 28, 517–538 (2020). https://doi.org/10.1007/s10485-019-09588-4

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