Abstract

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 higherrank 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.