  While homology theory of associative structures, such as groups and rings,
has been extensively studied in the past beginning with the work of Hopf,
Eilenberg, and Hochschild, homology of non-associative distributive structures,
such as quandles, were neglected until recently. Distributive structures have
been studied for a long time. In 1880, C.S. Peirce emphasized the importance of
(right) self-distributivity in algebraic structures. However, homology for
these universal algebras was introduced only sixteen years ago by Fenn, Rourke,
and Sanderson. We develop this theory in the historical context and propose a
general framework to study homology of distributive structures. We illustrate
the theory by computing some examples of 1-term, 2-term, and 3-term homology,
and then discussing 4-term homology for Boolean algebras and distributive
lattices. We outline potential relations to Khovanov homology, via the
Yang-Baxter operator.
