Simplification & Incidence: How an Incidence-focused Perspective Patches Category-theoretic Problems in Graph Theory
Year: 2024
Type: preprint
Abstract: By applying simplification operations to categories of multigraphs, several natural graph operations are shown to demonstrate categorical issues. The replacement of an undirected edge with a directed cycle for digraphs admits both a left and a right adjoint, while the analogous operation for quivers only admits a left adjoint. The clique-replacement graph, intersection graph, and dual hypergraph fail to be functorial with traditional graph homomorphisms. The three failures are remedied by considering weak set-system homomorphisms, which form a category isomorphic to both the category of incidence structures and a lax comma category.
Source: arXiv (Cornell University)
Author: Grilliette, Will
Institution: National Security Agency
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4393064151