You should keep ketchup in the fridge if you want too but it's not required.
Ideally you should keep ketchup at room temperature such as on the table, counter, in the pantry etc as it requires no refrigeration.
Ketchup should be kept in the cupboard or pantry or on the counter or table at room temperature.
Keeping ketchup in the refrigerator is just a waste of space in the refrigerator because ketchup does not require refrigeration.
You don't need to or have to refrigerate Ketchup.
Ketchup can safely be left out at room temperature.
You can refrigerate ketchup but there's no need to as the Ketchup won't spoil or go bad at room temperature.
Most condiments like Ketchup don't require refrigeration.
Ketchup does not need refrigeration and will keep for 6 months or even longer out at room temperature after opening it.
You can refrigerate the opened bottles of ketchup to keep them fresher longer but you do not have to refrigerate ketchup for it to keep.
Ketchup is basically just tomatoes made into the ketchup and as long as you keep the ketchup bottle closed when not using it the ketchup will last for a long time.
I never refrigerate my ketchup and a lot of restaurants do not refrigerate their ketchup either.
Of course the ketchup in restaurants is used up pretty quickly but there's still no need to refrigerate ketchup unless you want too.