I definitely agree that boss summoners should be grouped together in the same category.
As for the other two: I believe they should be in another category, but should be together in said category.
The first category, I believe, could be called "Summoners-Hostile" or the like. Similarly, the second category could be called "Summoners-Friendly" or the like. (Those classifications double as my reasoning for keeping the second class of summoning items grouped together – pets and minions may have different functions, but they are all still friendly NPCs.)
I agree with this but I think they should be seperated like the statues(functional/nonfunctional::vanity/utility/minion)