arXiv
Open Access
2024
Simplification & Incidence: How an Incidence-focused Perspective Patches Category-theoretic Problems in Graph Theory
Will Grilliette
Abstrak
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.
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Will Grilliette
Akses Cepat
Informasi Jurnal
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- 2024
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