If you have correctly setup your Core Data model, then you have a to-many relationship from the Category entity to the Item entity, and an inverse to-one relationship from Item to Category. Also, you have a "cascade" delete rule for the to-many relationship and a "nullify" delete rule for the to-one relationship.
Assuming this, each time you insert an Item object, setting its Category relationship automatically inserts the Item into the corresponding Category. Deleting an Item automatically removes it from the corresponding Category.
On the Category side, removing a Category automatically removes all of the corresponding Item objects.
Therefore, when you fetch Items, you have already fetched for each Item object its corresponding Category object. You do not need do anything else. Note that, by default, you are not actually retrieving the Category object during the fetch: instead a fault is fired the first time you try to access the object and the object is retrieved at that time. This provides better performances if you do not plan to use immediately the Category object stored within the Item object just fetched. If you plan to use the Category object almost every time you fetch an Item, then you must use the NSFetchRequest methods
- (void)setReturnsObjectsAsFaults:(BOOL)yesNo
- (void)setRelationshipKeyPathsForPrefetching:(NSArray *)keys
to tell Core Data that you do now want faults and that you ask for prefetching your Category relationship.