Joao Pita Costa: On the coset structure of a skew lattice.

ON THE COSET STRUCTURE OF A SKEW LATTICE*

Joao Pita Costa*

University of Ljubljana


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 revisit another approach to these algebras, namely the study of its coset structure, and relate the coset category derived from it with the poset category and lattice image of the respective skew lattice.

* The author thanks the support of Funda\c c\~ao para a Ci\^ encia e Tecnologia with the reference SFRH / BD / 36694 / 2007.