  We discuss the notion of a span of cospans and define, for them, horizonal
and vertical composition. These compositions satisfy the interchange law if
working in a topos $\mathbf{C}$ and if the span legs are monic. A bicategory is
then constructed from $\mathbf{C}$-objects, $\mathbf{C}$-cospans, and doubly
monic spans of $\mathbf{C}$-cospans. The primary motivation for this
construction is an application to graph rewriting.
