  Recently Galatius, Madsen, Tillmann and Weiss identified the homotopy type of
the classifying space of the cobordism category of embedded d-dimensional
manifolds [7] for each positive integer d. Their result lead to a new proof of
the generalized standard Mumford conjecture. We extend the main theorem of [7]
to the case of cobordism categories of embedded d-dimensional manifolds with
prescribed singularities, and explain the relation of singular cobordism
categories to the bordism version of the Gromov h-principle.
