A coalgebraic model of graphs

Abstract

For a set-endofunctor $F$, a graph is triple $(V,E,g)$ with a structure map $g:E\to FV$. 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.

arXiv comment6 pages, 5 figures