A coalgebraic model of graphs

TL;DR

This paper presents a coalgebraic framework for modeling graphs using set-endofunctors, providing a categorical perspective that generalizes traditional graph models and explores their properties.

Contribution

It introduces a novel coalgebraic model of graphs over the category of sets and analyzes the categorical properties of the resulting graph category.

Findings

Graphs modeled as coalgebras over Set×Set

Properties of the category of graphs derived from coalgebra theory

Generalization of graph models through coalgebraic structures

Abstract

For a set-endofunctor $F$, a graph is triple $(V,E,g)$ with a structure map $g:E\rightarrow F V$. This model is a generalized coalgebra over the category of sets. In this note, we model graphs as coalgebras over $Set\times Set$ and use the theory of coalgebras over arbitrary categories to conclude properties of the category of graphs.