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A New Characterisation of Goursat Categories

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Abstract

We present a new characterisation of Goursat categories in terms of special kind of pushouts, that we call Goursat pushouts. This allows one to prove that, for a regular category, the Goursat property is actually equivalent to the validity of the denormalised 3-by-3 Lemma. Goursat pushouts are also useful to clarify, from a categorical perspective, the existence of the quaternary operations characterising 3-permutable varieties.

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Authors and Affiliations

  1. Insitut de Recherche en Mathématique et Physique, Université Catholique de Louvain, Chemin du Cyclotron 2, 1348, Louvain-la-Neuve, Belgium

    Marino Gran

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

    Diana Rodelo

  3. Centre for Mathematics of the University of Coimbra, 3001-454, Coimbra, Portugal

    Diana Rodelo

Authors
  1. Marino Gran
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  2. Diana Rodelo
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Correspondence to Marino Gran.

Additional information

Research supported by the F.N.R.S. grant Crédit aux chercheurs 1.5.016.10F, and by FCT/Centro de Matemática da Universidade de Coimbra.

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Gran, M., Rodelo, D. A New Characterisation of Goursat Categories. Appl Categor Struct 20, 229–238 (2012). https://doi.org/10.1007/s10485-010-9236-x

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  • DOI: https://doi.org/10.1007/s10485-010-9236-x

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