\(C^*\)-correspondences for Ordinal Graphs
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Abstract: We consider \(C^*\)-algebras of categories we call ordinal graphs which generalize directed graphs by allowing paths to have ordinal length. We present criteria for when the \(C^*\)-algebra of an ordinal graph is naturally isomorphic to a Cuntz-Pimsner algebra. This condition also characterizes when certain homomorphisms from algebras of distinguished subcategories into the ordinal graph algebra are all simultaneously injective. We describe how an application of these results leads to a slight generalization of a previous Cuntz-Krieger uniqueness theorem.