  Hurwitz spaces are homotopy quotients of the braid group action on the moduli
space of principal bundles over a punctured plane. By considering a certain
model for this homotopy quotient we build an aspherical topological operad that
we call the little bundles operad. As our main result, we describe this operad
as a groupoid-valued operad in terms of generators and relations and prove that
the categorical little bundles algebras are precisely Turaev's crossed
categories. Moreover, we prove that the evaluation on the circle of a
homotopical two-dimensional equivariant topolological field theory yields a
little bundles algebra up to coherent homotopy.
