  This paper is a sequel to my essay "Distributivity versus associativity in
the homology theory of algebraic structures" Demonstratio Math., 44(4), 2011,
821-867 (arXiv:1109.4850 [math.GT]). We start from naive invariants of arc
colorings and survey associative and distributive magmas and their homology
with relation to knot theory. We outline potential relations to Khovanov
homology and categorification, via Yang-Baxter operators. We use here the fact
that Yang-Baxter equation can be thought of as a generalization of
self-distributivity. We show how to define and visualize Yang-Baxter homology,
in particular giving a simple description of homology of biquandles.
