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Duality in non-abelian algebra III. Normal categories and 0-regular varieties

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Abstract

Normal categories are pointed categorical counterparts of 0-regular varieties, i.e., varieties where each congruence is uniquely determined by the equivalence class of a fixed constant 0. In this paper, we give a new axiomatic approach to normal categories, which uses self-dual axioms on a functor defined using subobjects of objects in the category. We also show that a similar approach can be developed for 0-regular varieties, if we replace subobjects with subsets of algebras containing 0.

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Authors and Affiliations

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

    Zurab Janelidze & Thomas Weighill

  2. Department of Mathematics, University of Tennessee, Knoxville, TN, 37996, USA

    Thomas Weighill

Authors
  1. Zurab Janelidze
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  2. Thomas Weighill
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Correspondence to Zurab Janelidze.

Additional information

Presented by J. Adamek.

Supported by the South African National Research Foundation (both authors) and the MIH Media Lab at Stellenbosch University (second author).

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Janelidze, Z., Weighill, T. Duality in non-abelian algebra III. Normal categories and 0-regular varieties. Algebra Univers. 77, 1–28 (2017). https://doi.org/10.1007/s00012-017-0422-7

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  • DOI: https://doi.org/10.1007/s00012-017-0422-7

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