A finite quandle is simply connected exactly when it is principal and all prime-size abelian cocycles are trivial, which yields classifications for sizes p^2 and p^3.
A Universal algebraic approach to rack coverings
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abstract
We study rack and quandle coverings from a universal algebraic viewpoint and we show how they can be understood using the notion of strongly abelian congruences. We provide an abstract characterization of several particular types of covering extensions, such as central and abelian ones. 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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2025 1verdicts
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On Simply Connected Quandles
A finite quandle is simply connected exactly when it is principal and all prime-size abelian cocycles are trivial, which yields classifications for sizes p^2 and p^3.