  The class of skew lattices can be seen as an algebraic category. It models an
algebraic theory in the category of Sets where the Green's relation D is a
congruence describing an adjunction to the category of Lattices. In this paper
we will discuss the relevance of this approach, revisit some known
decompositions and relate the order structure of a skew lattice with its coset
structure that describes the internal coset decomposition of the respective
algebra.
