You know, one of the reason that notations differ is because that's useful. The symbol \times might mean cross product or direct product of groups, or cartesia

You know, one of the reason that notations differ is because that's useful. The symbol \times might mean cross product or direct product of groups, or cartesian product. Why? Because these operations are conceptually similar --- they all involve making a multiplicatively larger thing from smaller things. Using the same symbol for different things might be polymorphism, not conflict.