Ordinal graphs and their \(C^*\)-algebras
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We introduce a class of left-cancellative categories which generalizes the category of paths of a directed graph by allowing paths to have ordinal length. We use generators and relations to study the Cuntz-Krieger algebra defined by Spielberg. For each ordinal we construct an associated \(C^*\)-correspondence. Then we apply Eryüzlü and Tomforde’s condition (S) and obtain a Cuntz-Krieger uniqueness theorem for ordinal graphs.