A P0420 can be caused by a lot of things. As Mart said, the front and rear o2 readings are compared by the ecu. The front is used for fuel control and the rear is a catalyst monitor. Due to the way cats store oxygen the rear o2 reading should remain relatively steady, and only change significantly on full throttle, then again when letting off.
Things I've seen cause the code include using leaded petrol when the car should be run on unleaded (like all catalyst cars should), a car burning excessive oil and contaminating the cat, leaking fuel injectors causing the cat to start to melt, an exhaust leak either at the front o2 or near the rear o2, causing the readings to become similar to each other (though a leak near a front 02 usually results in a P0171 Bank 1 lean code also being set) and on older cars, the coolant temp sensor. The temp sensor causes this issue because it's used to tell the ecu when the car is warm enough to be able to trust the front o2 sensor. This is less likely on newer cars (last 15 years or so) as they have heated oxygen sensors that come up to temp in a matter of 30 seconds or so.
Before you try replacing the rear o2, get a scan tool with live data and see what's going on. If the rear o2 is switching in time with the front then I'd suspect the cat is bad.
Also note that while catalysts do go bad, quite often there is an underlying cause (as mentioned above). Replacing the catalyst and not taking care of the problem causing it to fail (if there is a problem ) will just kill the new catalyst too.
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