  Transit functions serve not only as abstractions of betweenness and convexity
but are also closely connected with clustering systems. Here, we investigate
the canonical transit functions of binary clustering systems inspired by
pyramids, i.e., interval hypergraphs. We provide alternative characterizations
of weak hierarchies, and describe union-closed binary clustering systems as a
subclass of pyramids and weakly pyramidal clustering systems as an interesting
generalization.
