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A short introduction to clones. (English) Zbl 1341.08003

Power, John (ed.) et al., Proceedings of the workshop on algebra, coalgebra and topology (WACT 2013), Bath, UK, March 1, 2013. Amsterdam: Elsevier. Electronic Notes in Theoretical Computer Science 303, 107-120, electronic only (2014).
Summary: In universal algebra, clones are used to study algebras abstracted from their signature. The aim of this paper is to give a brief introduction to the theory thereof. We give basic definitions and examples, and we present several results and open problems, selected from almost one hundred years of ongoing research. We also discuss what is arguably the most important tool to study clones – the Galois connection between operations and relations built on the notion of preservation. We conclude the paper by explaining the connection between clones and the closely related category theoretic notion of Lawvere theory.
For the entire collection see [Zbl 1310.68019].

MSC:

08A40 Operations and polynomials in algebraic structures, primal algebras
06A15 Galois correspondences, closure operators (in relation to ordered sets)
18C10 Theories (e.g., algebraic theories), structure, and semantics
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