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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.13165 |
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Table of Contents:
- 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.