We continue the study of the quandle of homomorphisms into a medial quandle begun in . We show that it suffices to consider only medial source quandles, and therefore the structure theorem of  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
Bonatto, Marco, et al. “On the Structure of Hom Quandles.” Journal of Pure and Applied Algebra, Jan. 2019.