So you've got your basic table:
Artwork
ID
Name, artist, etc., etc.
And probably you should have a Subcategory table
Subcategory
ID
Name, etc. etc
You need a 'Many to Many' Table to link the two:
Artwork_Subcategory:
ArtworkID
SubcategoryID
When you submit the artwork, you'll probably use a SELECT with the attribute MULTIPLE. You'll name it something like subs[], being sure to use brackets in the name.
Then when the form is submitted you can check $_POST ['subs[]']
It will contain an array of all the subcategories selected.
Then you insert all the subcategories for the artwork into Artwork_Subcategory.
To find all the artwork for a subcategory:
SELECT Artwork.* from Artwork, Artwork_Subcategory WHERE ArtworkID=Artwork.ID and SubcategoryID=2
Hope this gets you started. THere are books and Web Tutorials about this: Google: Relational Database Programming SQL Tutorial