A Universal algebraic approach to rack coverings
arXiv:1910.09317
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.
References in corpus (7)
- Set-theoretical solutions to the quantum Yang-Baxter equation
- On set-theoretical solutions of the quantum Yang-Baxter equation
- Nichols algebras of group type with many quadratic relations
- The retraction relation for biracks
- Quandle coloring and cocycle invariants of composite knots and abelian extensions
- On factorisation systems for surjective quandle homomorphisms
- Involutive latin solutions of the Yang-Baxter equation