In K2 Management site, you cannot move SmartObjects between categories since the Move function is disabled, even though you have the rights to complete the action. You are also unable to rename a category as the Rename option is also disabled.
This is a known issue in K2 Five 5.1, and the fix is included in the latest update.
This issue is fixed in K2 Five 5.1 FP5: http://help.k2.com/kb002505
Please submit a support ticket to obtain the fix pack.