State transitions as morphisms for complete lattices

TL;DR

This paper introduces a new type of morphism called 'state transitions' for complete lattices, expanding their categorical framework and comparing it with quantaloidal enrichments to deepen the understanding of their structure.

Contribution

It proposes enlarging the hom-sets of complete lattices by incorporating state transitions and compares this with existing quantaloidal enrichment frameworks.

Findings

Enlarged category of complete lattices with state transitions

Comparison with functorial quantaloidal enrichment

Comparison with contextual quantaloidal enrichment in Parset

Abstract

We enlarge the hom-sets of categories of complete lattices by introducing `state transitions' as generalized morphisms. The obtained category will then be compared with a functorial quantaloidal enrichment and a contextual quantaloidal enrichment that uses a specific concretization in the category of sets and partially defined maps ($Parset$).