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A general Galois theory for operations and relations in arbitrary categories

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In this paper, we generalize the notions of polymorphisms and invariant relations to arbitrary categories. This leads us to a Galois connection that coincides with the classical case from universal algebra if the underlying category is the category of sets, but remains applicable no matter how the category is changed. In analogy to the situation in the classical case, we characterize the Galois closed classes by local closures of clones of operations and local closures of what we will introduce as clones of (generalized) relations. Since the approach is built on purely category-theoretic properties, we will also discuss the dualization of our notions.

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  1. Institut für Algebra, Technische Universität Dresden, 01069, Dresden, Germany

    Sebastian Kerkhoff

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  1. Sebastian Kerkhoff
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Presented by A. Szendrei.

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Kerkhoff, S. A general Galois theory for operations and relations in arbitrary categories. Algebra Univers. 68, 325–352 (2012). https://doi.org/10.1007/s00012-012-0209-9

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