On the Structure of Hom Quandles

Abstract

We continue the study of the quandle of homomorphisms into a medial quandle begun in Crans and Nelson. We show that it suffices to consider only medial source quandles, and therefore the structure theorem of Jedlicka et al. provides a characterization of the Hom quandle. In the particular case when the target is 2-reductive this characterization takes on a simple form that makes it easy to count and determine the structure of the Hom quandle.