A new perspective on categorical skew lattices with examples

It was recently published, in the research journal Demonstratio Mathematica, a new paper on the coset category of skew lattices. The coset structure decomposition is an original approach to the study of these algebras describing the relation between its rectangular classes. In this paper, we will look at the category determined by these rectangular algebras and the morphisms between them, showing that not all skew lattices can determine such a category. Furthermore, we will present a class of examples of skew lattices in rings that are not strictly categorical, and present sufficient conditions for skew lattices of matrices in rings to constitute ^-distributive skew lattices.

The reference to this paper is the following:

Joao Pita Costa. On the Coset Category of a Skew Lattice. Demonstratio Mathematica. Vol. XLVII No. 3 (2014) : 539--554

This paper is also available at the arXiv at http://arxiv.org/abs/1307.1567