Entropic Niebrzydowski tribrackets

In this paper, we introduce the notion of entropic Niebrzydowski tribrackets or just entropic tribrackets, analogous to entropic (also known as abelian or medial) quandles and biquandles. We show that if [Formula: see text] is a finite entropic tribracket then for any tribracket [Formula: see text], the homset [Formula: see text] (and in particular, for any oriented link [Formula: see text], the homset [Formula: see text]) also has the structure of an entropic tribracket. This operation yields a product on the category of entropic tribrackets; we compute the operation table for entropic tribrackets of small cardinality and prove a few results. We conjecture that this structure can be used to distinguish links which have the same counting invariant with respect to a chosen entropic coloring tribracket [Formula: see text].