Categorical skew lattices

TL;DR

This paper studies categorical skew lattices, a special class of skew lattices with well-behaved partial orders, characterized by forbidden subalgebras, and explores the subclass of strictly categorical skew lattices.

Contribution

It characterizes categorical skew lattices via forbidden subalgebras and introduces the subclass of strictly categorical skew lattices.

Findings

Categorical skew lattices are characterized by a countable family of forbidden subalgebras.

Most skew lattices of interest are categorical, but not all.

The paper explores the properties of strictly categorical skew lattices.

Abstract

Categorical skew lattices are a variety of skew lattices on which the natural partial order is especially well behaved. While most skew lattices of interest are categorical, not all are. They are characterized by a countable family of forbidden subalgebras. We also consider the subclass of strictly categorical skew lattices.