Why cannot I add attributes to a category ?, Add category attributes?

Why cannot I add attributes to a category ?, Add category attributes?
To declare an attribute using @ property in a category, add the attribute to the attribute list of the class and declare the setter and getter methods, but no corresponding member variables are generated, the setter and getter methods are not implemented either. In addition, an error is reported using the dot syntax. Therefore, attributes cannot be added to a category. However, after @ property is declared in the classification, the setter and getter methods are implemented. In this case, you can assign values and values to this attribute through the dot syntax. That is to say, after using @ property to declare attributes in a category and implementing the setter and getter methods, you can consider that attributes are added to this class. Source: bytes