A Universal algebraic approach to rack coverings

arxiv(2019)

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摘要
We study rack coverings from a universal algebraic viewpoint and we prove that they can be understood using the notion of strongly abelian congruence. We investigate and characterize several particular classes of coverings as central and abelian coverings and coverings preserving the displacement group. %We also compare our approach with the categorical approach used in different paper. We give a new characterization of simply connected quandles and we show that the categorical notion of normal extension coincides with the notion of central covering. We answer several questions from the papers of Clark, Saito and Vendramin \cite{CS} and \cite{CSV} about identities preserved by quandle coverings.
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