The category of symmetric quandles is a Mal'tsev variety whose subvariety of abelian symmetric quandles is the category of abelian algebras. We give an algebraic description of the quandle extensions that are central for the adjunction between the variety of quandles and its subvariety of abelian symmetric quandles.
Keywords: Quandle, symmetric quandle, abelian object, Mal'tsev variety, central extension, categorical Galois theory
2010 MSC: 57M27, 08B05, 18A20, 13B05
Theory and Applications of Categories, Vol. 31, 2016, No. 8, pp 201-216.