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Abstract

We show that varietal techniques based on the existence of operations of a certain arity can be extended to n-permutable categories with binary coproducts. This is achieved via what we call approximate Hagemann–Mitschke co-operations, a generalisation of the notion of approximate Mal’tsev co-operation [2]. In particular, we extend characterisation theorems for n-permutable varieties due to J. Hagemann and A. Mitschke [8, 9] to regular categories with binary coproducts.

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Correspondence to Tim Van der Linden.

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Dedicated to George Janelidze on the occasion of his sixtieth birthday

The first author was supported by Centro de Matemática da Universidade de Coimbra (CMUC), funded by the European Regional Development Fund through the program COMPETE and by the Portuguese Government through the FCT–Fundação para a Ciência e a Tecnologia under the project PEst-C/MAT/UI0324/2013 and grants number PTDC/MAT/120222/2010 and SFRH/BPD/69661/2010. The second author works as chercheur qualifié for Fonds de la Recherche Scientifique–FNRS and would like to thank CMUC for its kind hospitality during his stays in Coimbra.

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Rodelo, D., Van der Linden, T. Approximate Hagemann–Mitschke Co-operations. Appl Categor Struct 22, 1009–1020 (2014). https://doi.org/10.1007/s10485-013-9359-y

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  • DOI: https://doi.org/10.1007/s10485-013-9359-y

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