The object that instantiated them might not be around for long, so it would be a bit dangerous for the objects to know about it. You could pass a pointer to the appController, if that's really what you need, but unless you retain the controller, there is no guarantee it is going to be around, and you should absolutely NOT retain the controller, because you'll probably get a retain cycle, that is if the controller has retained the object. But there might be other ways of accomplishing what you want to do, maybe more obj- C-friendly. So the question is, what are you trying to accomplish?
Or presumed your controller is a singleton, you can implement an extra accessor owner-level, like @implementation MyController static MyController myself=null; -init { // or awakeFromNib, or whatever method you use for initialization ... return myself=self; } +(MyController*)sharedController { return myself; } ... and the worker would use [MyController sharedController] to access the thing.
You could pass it as a parameter to the object's -init... method(s). You could add a set... method to the class and call it from the AppController. If the object is instantiated in a nib, you could make the member variable an outlet, and connect it in IB.