Abstract

Results of Fowler and Sims show that every kgraph is completely determined by its kcoloured skeleton and collection of commuting squares. Here we give an explicit description of the kgraph associated with a given skeleton and collection of squares and show that two kgraphs 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 kgraph. is isomorphic to the quotient of the path category of its skeleton by the equivalence relation determined by the commuting squares, and show that this extends to a homeomorphism of infinitepath spaces when the kgraph is row finite with no sources. We conclude with a short direct proof of the characterization, originally due to Robertson and Sims, of simplicity of the C*algebra of a rowfinite kgraph with no sources.