The equality and relational operators (==, !=, <=>, >, >=, <, and <=) can not be overridden by a Category method. Though a direct call to the equals() or compareTo() methods does use the Category method (except for the Number.compareTo(Number) case which does not call the Category method).
It would be desirable to support overriding of the equality and relational operators, both for completeness and utility's sake. This would complement the ability to override the mathematical operators (i.e. +, -, *, /, etc.) via Category methods. In particular it would allow the comparison of object types where the equals() and compareTo() methods don't directly support the desired type combinations.
The included category and test demonstrates some of the cases in question. The OperatorCategoryTest class contains tests that demonstrate successful uses and failing ones.