The server log tool may display all or only some categories.
You cannot guess it.
The title of the tool should display that.
The tool should be multiinstance depending on the current category.

E.G.
1) open the ServerLogTool.
2) Launch a full live rebuild.
3) silently the ServerLogTool is reopened but limited to one category.

I would like that a second tab is displayed with title "Log of live rebuild"