Accorinding to the Open/Closed principle
. . . software entities (classes, modules, functions, etc.) should be open for extension, but closed for modification
So can I say that the Category is a strong violation to this principle?
I don't see how. Categories allow you to add functionality which depends on the existing interface. They don't allow you to make any real changes to the original class, they just provide some syntactic sugar which gives you the illusion that new methods have been added to the class.
In other words, categories help you extend a class. They do not modify it. Seems like they reinforce the open/closed principle.