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.