A characterization of central extensions in the variety of quandles

Valérian Even, Marino Gran and Andrea Montoli

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.

Published 2016-04-02.


TAC Home