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Closure operators and central extensions in the category of quandles

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If you have a question about this talk, please contact Dr Ignacio Lopez Franco .

In this talk we shall present some recent results concerning the categorical properties of quandles. These algebraic structures, which are of interest in knot theory, form a variety of universal algebras. We shall first study the properties of the closure operators corresponding to the reflector from the variety of quandles to its subvariety of trivial quandles. The algebraically connected quandles are shown to be exactly the c-connected objects for the induced regular closure operator c, while the trivial quandles are the c-separated objects. Finally, the central extensions of quandles corresponding to the reflector to the subvariety of abelian symmetric quandles will be described. The talk will be based on joint work with Valérian Even and Andrea Montoli.

This talk is part of the Category Theory Seminar series.

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