To be of some value in physics, there should be some uniqueness. The correct version of " parallel transport for particles, strings and 2-branes " would be expected to have some extra condition forcing D=11. It should relate to Evans paper on the link between division algebras and supersymmetry, and pass to topology via the link between division algebras, projective spaces and Hopf fibrations.On the other hand, Schreiber  has argued that for any Lie 2-group G , the
3-group I N N (G ) allows us to deﬁne a version of parallel transport for particles, strings and 2-branes starting from an arbitrary g-valued 1-form A and h-valued 2-form B. The condition dt(B) = F is not required. So, to treat 4d Palatini gravity as a higher gauge theory, perhaps we can treat the basic ﬁelds as a 3-connection on an I N N (T SO(3, 1))-3-bundle. To entice the reader into pursuing this line of research, we optimistically dub this 3-group I N N (T (SO(3, 1)) the gravity 3-group.