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On Algebraic and More General Categories Whose Split Epimorphisms Have Underlying Product Projections

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Abstract

We characterize those varieties of universal algebras where every split epimorphism considered as a map of sets is a product projection. In addition we obtain new characterizations of semi-abelian, protomodular, unital and subtractive varieties as well as varieties of right Ω-loops and biternary systems.

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Authors and Affiliations

  1. Department of Mathematical Sciences (Mathematics Division), University of Stellenbosch, Private Bag X1, Matieland, 7602, South Africa

    J. R. A. Gray

  2. Departamento de Matemática, Escola Superior de Tecnologia e Gestão, Centro para o Desenvolvimento Rápido e Sustentado do Produto,, Instituto Politécnico de Leiria, Leiria, Portugal

    N. Martins-Ferreira

Authors
  1. J. R. A. Gray
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  2. N. Martins-Ferreira
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Corresponding author

Correspondence to J. R. A. Gray.

Additional information

N. Martins-Ferreira’s research was supported by IPLeiria(ESTG/CDRSP) and FCT grant SFRH/BPD/43216/2008. Also by the FCT projects: PTDC/EME-CRO/120585/2010, PTDC/MAT/120222/2010 and PEst-OE/EME/UI4044/2013.

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Gray, J.R.A., Martins-Ferreira, N. On Algebraic and More General Categories Whose Split Epimorphisms Have Underlying Product Projections. Appl Categor Struct 23, 429–446 (2015). https://doi.org/10.1007/s10485-013-9336-5

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  • DOI: https://doi.org/10.1007/s10485-013-9336-5

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