The cat is on the non-electronic engines and does remove NOX. The newer common rail engines also use a cat.

 

The CAT is short for catalyst, It's main function is to burn up HC emissions. HC is a product of combustion just like NOX, co, co2, and on diesels smoke or particulates. When the injectors start to coke up and drip a little they produce higher HC and smoke. The CAT absorbs the heat from the exh and concentrates it and burns up the HC and some of the smoke. NOX is produced from heat and pressure during combustion. The more adv the timing is the more NOX is produced. When the timing is retarded some it reduces NOX and produces more heat in the exh and makes the CAT run hotter and is more efficient in cleaning up the exhaust emmissions. Injectors start coking up some after only a few thousand miles and more so when it is run easy. Fuel conditioner will help reduce that. The EPA says it is a problem and is forcing the auto companies to clean them up. They are also working on Particulate traps to filter out the somke from diesel exhaust and burn them up. There are a fleet of semi's running around with experimental traps now to see how they work and hold up. They will be comming soon too.
Sorry to be so long winded. I did R&D at GM in the dyno labs for 14 yrs in the 70's and early 80's. 4 of those years were on diesel inj and comb development including combustion photography on a running motor.