Please, permit me this comment:
Both of you are right by disagreeing!
Polyurethane is not polyester but a polyester polyurethane is a polyester, too. Especially, if ester groups quite more than carbamate ones, e.g. a polyurethane polymer that is prepared from poly(ethylene succinate) 10,000.
Besides, a carbamate group is half an amide and half an ester that can be hydrolyzed, hydrogenated, transesterified, transamidated, etc.