Actually, I am not in Shanghai, I am in Shenzhen, but that is ok. I think I can give you some insight.
You "can" bring your kitty to China and Shanghai specifically, BUT it will require a bunch of red tape you may not like. The link below offers some guidance:
http://www.scaashanghai.org/china_pet_import_procedure.shtml
Now on a personal note, I would say don't do it. Not only does it require additional money, a pet passport, full documentation and proof of vaccinations, and the like, but you must understand, cats are not considered a welcome pet here. In fact most cats are considered pests, on the scale of rats on cockroaches. 95% of the cats you see in China are feral, wild cats. Very dirty and unhealthy. I would NEVER EVER EVER let a pet cat outside here!!!! EVER! The wild cats would eat it or the management companies would poison it. Period.
Also, you may remember a little issue called SARS, which was determined to have been spread via the feral cat population. So not only were millions of sick kitties culled, they also received a very negative stigma. Dogs are a different story, they are easily the most common and popular pet in China, but I have never, in 7 years, even met a person with a pet cat here....
You can however buy all the most popular cat foods, toys and supplies, you just might have to hunt a little more for them.
That brings me to my final point. Whereas you may have (with some added hassle) the ability to bring kitty in, you may have a MUCH harder time getting it out again.
If you are only coming for a short term (1 year or less) and you don't want kitty to be a 100% house cat, never going outside, I would say leave kitty at home with someone who will love it. Much easier for you and better for kitty in my opinion.
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