Looking for specific shopping list app

Hi,

I'm trying to find an app for creating my weekly shopping list.

There are tons of them but so far I haven't found one with these specific features:

1. Must allow syncing among devices
2. The database must be editable by the user: add/modify/delete categories and products
3. Each product and category in the database must allow a (small) picture or thumbnail.
4. The list must include the product name, its picture and a tickbox

Anyone?