2024/03/19 by Will Grilliette, Grilliette, Will
Computer Science · #05C20 #05C65 #18A25 #18A40 #Category Theory (math.CT) #Combinatorics (math.CO) #Data Visualization and Analytics #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2403.13165
openalex publication_date 2024/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.