# Towards a Categorical Representation of Reversible Event Structures

## TL;DR

This paper develops a categorical framework for reversible event structures, extending traditional models of concurrency to reversible computing and exploring their properties and subcategories.

## Contribution

It introduces categorical models for reversible event structures, including functors, products, and co-products, and defines cause-respecting subcategories for reversible computing.

## Key findings

- Existence of products and co-products in many cases
- Categorical formulation of reversible event structures
- Definition of cause-respecting subcategories

## Abstract

We study categories for reversible computing, focussing on reversible forms of event structures. Event structures are a well-established model of true concurrency. There exist a number of forms of event structures, including prime event structures, asymmetric event structures, and general event structures. More recently, reversible forms of these types of event structures have been defined. We formulate corresponding categories and functors between them. We show that products and co-products exist in many cases. In most work on reversible computing, including reversible process calculi, a cause-respecting condition is posited, meaning that the cause of an event may not be reversed before the event itself. Since reversible event structures are not assumed to be cause-respecting in general, we also define cause-respecting subcategories of these event structures. Our longer-term aim is to formulate event structure semantics for reversible process calculi.