Ignore my Question. 

I found out how to resolve it: 

situation: I had managed to accidentally delete the top most eCommerce category in my Shop. What that suddenly did was to show ALL products in a total mess.  Panic!  Of course it is obvious what has happened: the eCommerce category/ies entries have been deleted from *every* product.

So you go back to each Product in the Inventory. Do not touch the Product Category in General Information. That has nothing to do with the eCommerce shop. You instead click on the 'Sales' tab.  In the 'Sales tab' then  select 'Categories'. You'll probably see it is empty! So now: re-create the category here.  Say you had a structure which was showing All / Furniture / Desks /.   Then you will need to first create 'Furniture' with no parent. This will automatically hook up to the 'All Products'.  Then create 'Desks' but this time select parent is 'Furniture'. Now you have recreated the hierarchy. Phew!

Don't forget to Publish the product or you won't see your results.  

Then you see the shop category menu start to form again.  

I hope this helps some poor person burning the midnight oil trying to fix this stuff. Enjoy and good luck!