Grocery/List app for iOS with decent web application I am looking for a descent iOS application that will allow me to sync my grocery list between my wife and I. I would like a solution that has a web application that we can use to enter all of our grocery items. I have tried many apps but there are so many out there now I may have missed some. The main features I am looking for are ... 


Synchronization between devices and web app
Push notification when list updated from device or web app
Photo support (so I can get the correct item)
Ordering items on a per store basis (Walmart has items organized differently than Stop-n-Shop)
List items by category (Breads, Deli, Dairy, etc ..)
Multiple lists and stores


Here is a list of apps I have tried that may be of use to others.

Grocery Gadget - Nice UI on iOS but the web app is abysmal in speed. It takes about 10 seconds to update/delete a single item from the list. Web app freezes regularly.

Grocery IQ - No photo support; Web App looks nice though. Adds "sponsored items" to my list without asking.

Easy Shop Pro - No Web App; No Photo support

Shopping List - No Web App; No Photo support

Splash Shopper - Local WiFI sync only

Shopper Pro - Email based sync. No Push notification. Web app has major bugs.

Buy me a Pie! - Cannot categorize items in web app. Web app is very "bare bones"

I certainly don't mind paying for a good application so it does not need to be free.
Take a look at Catch. It was recently one of the featured apps on the App Store. It's not designed for shopping per se, but it can do everything but #2. Instead of a push notification, it silently updates. It does do notifications, but those are based on timed events.
It supports spaces and hashtags for categorization, which I think would fit your needs.

Also, it has a feature to share lists between people. If Catch doesn't cut it, you might want to look at Wunderlist also. Different, but many of the same features.

And, no, I have no connection to them, just like the app.

Update/Edit: Catch is no longer available. Wunderlist is better than ever, and Shopit the app is currently very hot (it's on the top free apps list in the U.S.) which does everything you asked about except sharing.