Looking through a Window based application ive used to experiment with as a way of getting my head around core data, ive noticed that the appdelegate has the following code

myAppDelegate.h

#import <UIKit/UIKit.h>
#import <CoreData/CoreData.h>

@interface iCaptureFreeAppDelegate : NSObject <UIApplicationDelegate> {


NSManagedObjectModel *managedObjectModel;
NSManagedObjectContext *managedObjectContext;       
NSPersistentStoreCoordinator *persistentStoreCoordinator;

UIWindow *window;
UITabBarController *tabBarController;

}

myAppDelegate.m

#import "myAppDelegate.h"


@interface iCaptureFreeAppDelegate (PrivateCoreDataStack)
@property (nonatomic, retain, readonly) NSManagedObjectModel *managedObjectModel;
@property (nonatomic, retain) NSManagedObjectContext *managedObjectContext;
@property (nonatomic, retain, readonly) NSPersistentStoreCoordinator *persistentStoreCoordinator;
@end

@implementation iCaptureFreeAppDelegate

@synthesize window, tabBarController;

// code ....

// 
- (NSManagedObjectContext *) managedObjectContext {
}
- (NSManagedObjectModel *)managedObjectModel {
}
- (NSPersistentStoreCoordinator *)persistentStoreCoordinator {
}

// etc.....

i want to understand a few things about what this project is doing

1. why the properties in the category declaration? (if i delete the privateCoreDataStack category everything still works...)
2. why the properties appear to be linked with the methods in the implementation ... managedObjectContext {} etc
3. why the members in the .h file have the same name as the properties and the methods
4. why code completion lets me use dot '.' to access the members but then fails on compilation say it cant find a getter

thanks !