# Remarks on some fundamental results about higher-rank graphs and their C*-algebras

@article{Hazlewood2011RemarksOS, title={Remarks on some fundamental results about higher-rank graphs and their C*-algebras}, author={Robert Hazlewood and Iain Raeburn and Aidan Sims and Samuel B. G. Webster}, journal={Proceedings of the Edinburgh Mathematical Society}, year={2011}, volume={56}, pages={575 - 597} }

Abstract Results of Fowler and Sims show that every k-graph is completely determined by its k-coloured skeleton and collection of commuting squares. Here we give an explicit description of the k-graph associated with a given skeleton and collection of squares and show that two k-graphs are isomorphic if and only if there is an isomorphism of their skeletons which preserves commuting squares. We use this to prove directly that each k-graph Λ is isomorphic to the quotient of the path category of…

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