Category of asynchronous systems and polygonal morphisms

TL;DR

This paper studies weak asynchronous systems modeled as trace monoids with partial actions, introducing polygonal morphisms that preserve structure, and proves the category of such systems has all limits and colimits.

Contribution

It defines polygonal morphisms between weak asynchronous systems and establishes that their category has all limits and colimits, enriching the theoretical framework.

Findings

Polygonal morphisms commute with actions and preserve event independence.

The category of weak asynchronous systems with these morphisms has all limits and colimits.

Provides foundational results for the categorical study of asynchronous systems.

Abstract

A weak asynchronous system is a trace monoid with a partial action on a set. A polygonal morphism between weak asynchronous systems commutes with the actions and preserves the independence of events. We prove that the category of weak asynchronous systems and polygonal morphisms has all limits and colimits.