  Let $(M_i, g_i)_{i \in \mathbb{N}}$ be a sequence of spin manifolds with
uniform bounded curvature and diameter that converges to a lower dimensional
Riemannian manifold $(B,h)$ in the Gromov-Hausdorff topology. Lott showed that
the spectrum converges to the spectrum of a certain first order elliptic
differential operator $\mathcal{D}$ on $B$. In this article we give an explicit
description of $\mathcal{D}^B$. We conclude that $\mathcal{D}^B$ is
self-adjoint and characterize the special case where $\mathcal{D}^B$ is the
Dirac operator on $B$.
