  Given any category $\mathcal{C}$ with pullbacks and a terminal object, we
show that the data consisting of the objects of $\mathcal{C}$, the spans of
$\mathcal{C}$, and the isomorphism classes of spans of spans of $\mathcal{C}$,
forms a bicategory. We denote this bicategory Span$_2(\mathcal{C})$ and show
that this construction can be applied to give a bicategory of $n$-manifolds,
cobordisms of those manifolds, and cobordisms of cobordisms.
