2007/12/07 by Alex Kumjian, Kumjian, Alex, David Pask +3 · 1 citation
Mathematics · #46L05 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L05
paper · pdf · doi:10.48550/arxiv.0712.1072
27 pages, four pictures drawn with Tikz. Version 2: title changed and numerous minor corrections and improvements. This version to appear in Trans. Amer. Math. Soc
openalex publication_date 2007/12/07 · arxiv created 2010/06/09 · arxiv updated 2010/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Λ↦ C*(Λ) to a functor from this category to the category whose objects are C*-algebras and whose morphisms are isomorphism classes of C*-correspondences.