Generalised morphisms of k-graphs: k-morphs

Details Generalised morphisms of k-graphs: k-morphs Generalised morphisms of k-graphs: k-morphs

2007-12-07

arxiv.org/abs/0712.1072v2

Mathematics

Operator Algebras

27 pages, four pictures drawn with Tikz. Version 2: title changed and numerous minor corrections and improvements. This versio

Scientific paper

In a number of recent papers, (k+l)-graphs have been constructed from k-graphs by inserting new edges in the last l dimensions. These constructions have been motivated by C*-algebraic considerations, so they have not been treated systematically at the level of higher-rank graphs themselves. Here we introduce k-morphs, which provide a systematic unifying framework for these various constructions. We think of k-morphs as the analogue, at the level of k-graphs, of C*-correspondences between C*-algebras. To make this analogy explicit, we introduce a category whose objects are k-graphs and whose morphisms are isomorphism classes of k-morphs. We show how to extend the assignment \Lambda \mapsto C*(\Lambda) to a functor from this category to the category whose objects are C*-algebras and whose morphisms are isomorphism classes of C*-correspondences.

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