A generalization of higher rank graphs

We introduce what we call `generalized higher rank $k$-graphs’ as a class of categories equipped with a notion of size. They extend not only the higher rank $k$-graphs, but also the Levi categories introduced by the first author as a categorical setting for graphs of groups. We prove that examples of generalized higher rank $k$-graphs can be constructed using Zappa-Sz'ep products of groupoids and higher rank graphs.