Objective-c – Override a method via ObjC Category and call the default implementation

There isn't, as others have already said, such a thing as a private method in Objective-C. However, starting in Objective-C 2.0 (meaning Mac OS X Leopard, iPhone OS 2.0, and later) you can create a category with an empty name (i.e. @interface MyClass ()) called Class Extension. What's unique about a class extension is that the method implementations must go in the same @implementation MyClass as the public methods. So I structure my classes like this:

In the .h file:

@interface MyClass {
    // My Instance Variables
}

- (void)myPublicMethod;

@end

And in the .m file:

@interface MyClass()

- (void)myPrivateMethod;

@end

@implementation MyClass

- (void)myPublicMethod {
    // Implementation goes here
}

- (void)myPrivateMethod {
    // Implementation goes here
}

@end

I think the greatest advantage of this approach is that it allows you to group your method implementations by functionality, not by the (sometimes arbitrary) public/private distinction.

To extend on drawnonward answer:

It's matter of hierarchy. Categories are really just a means of organizing source files. When compiled, all the methods of a class, including the ones defined in any category, end up in the same file.

Anything you could do in a regular class interface you can do in a category and anything you shouldn't do in a regular class interface you shouldn't do in a category.

So:

Category methods should not override existing methods (class or instance)

You can use methods defined in the regular class interface to override inherited methods so you can override inherited methods in a category.

However, you would never try to have to two identical method definitions in the same ordinary interface so you should never have a method in a category that has the same name as a method in either the ordinary interface or another category on the same class. Since all the method definitions end up in the same compiled file, they would obviously collide.

Two different categories implementing the same method results in undefined behavior

That should be rewritten to say "Two different categories implementing the same method for the same class results in undefined behavior." Again, because all the methods for any one class end up in the same file, having two methods in the same class would obviously cause weirdness.

You can use categories to provide methods that override superclass methods because a class and its superclass are two distinct classes.

If your ever confused about whether a category will cause problem just ask yourself this: "Would the methods in the category work if I copied and pasted them all into the class' .h/.m files?" If the answer is "yes" then you're in the clear. If "no", then you've got problems.