A functorial approach defines (X,M)-graphs in presheaf toposes for monoid actions, proves unfixed edges are necessary for exponentials and effective equivalence relations, and yields nerve-realization adjunctions for interpretations in arbitrary cocomplete categories.
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Functorial Approach to Graph and Hypergraph Theory
A functorial approach defines (X,M)-graphs in presheaf toposes for monoid actions, proves unfixed edges are necessary for exponentials and effective equivalence relations, and yields nerve-realization adjunctions for interpretations in arbitrary cocomplete categories.