  A crossed module is (A,H,d,\la) where d:A\to H is a homomorphism of groups
and H acts on A, with conditions leading to a groupoid A\lcross H{\to\atop
\to}H as an example of a strict 2-group. We give the corresponding notion of a
quantum 2-group where we replace the above by Hopf algebras and introduce a new
version of quantum groupoid. The work also suggests a natural notion of braided
crossed module where A a braided-Hopf algebra in the braided category
Z({}_H\CM) of crossed H-modules, although without the full groupoid picture in
this more general case.
