There is no specific object designed in the system. This is one of the design elements that you create depending on how you want to use it? No matter which approach you take, the first thing you need to do is create a relationship between the Group object (not Support Group) and the Incident Category object. This will allow you to add a drop down list of groups to the Incident Category window. Having updated the window, you can go into each of your categories and select the group the is linked to that category.
How you use this is then up to you. The least messy way, ie not using Copy Settings, is to add an assigment step into your process that uses value type to define the Group being assigned to as the group defined in the Incident category.
Hope this points you in the right direction.
sorry for late response, thanks for your suggestion. It's very helpfull.