Q-learning is a temporal-difference method and Monte Carlo tree search is a Monte Carlo method. In what category is MiniMax?
I think you are looking at it from the wrong direction, min-max is just a planning algorithm, decision strategy, in the sense that you are describing other algorithms/methods it does not have a category. For example, you have negamax algorithm which is in a sense the same thing the Monte Carlo Search Tree is to Monte Carlo. Min-max category is game theory really.
Now you should be thinking about RL algorithms in another way, and this is taxonomy:
So if you think about methods, you mentioned, let's put them in the right place:
- TD methods in general - model free
- Monte Carlo methods - model free
- MinMax - model-based (that could be discussed but it definitely needs access to a world model)