Algebra universalis

, 66:277 | Cite as

Categorical (binary) difference terms and protomodularity

Article

Abstract

In this paper we obtain an intrinsic syntactical characterization of protomodularity, via so-called categorical difference terms, similar to the one known in the case of varieties involving binary terms d satisfying d(x, x) = d(y, y). We also show that purely categorical modifications of the condition in the characterization give characterizations of Mal’tsev and additive categories, thus revealing a new conceptual link between these three classes of categories, and hence, also between the corresponding classes of varieties.

2010 Mathematics Subject Classification

Primary: 08B05 Secondary: 18C99 18E05 

Keywords and phrases

protomodular category Mal’tsev category naturally Mal’tsev category additive category categorical term algebraic modus ponens 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Pures et AppliquéesUniversité du LittoralCalaisFrance
  2. 2.Mathematics Division, Department of Mathematical SciencesStellenbosch UniversityStellenboschSouth Africa

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