How is Material Category Assignment to a Item in Master and Child Orgs controlled?

 If we assign category to an Item and assign it to a child Org , does it mean that the item category assignment is also copied to the child Org? If we want to control the category assignment between Parent and Child Org how would we do it?

If we change the Category assignment at master org, does it reflect on the Child Org? It would be great if someone can explain how the category assignment is controlled.