I have a database project, historic building materials...

I've designed 4 Tables like this (there are more fields which I didn't
listed here):
table products
- primary key(productid)
- product description
table category
- primary key(categoryid)
- category description
table subcategory
- primary key (Subcatid)
- subcatdescription
table subtype
- primary key (suptypeid)
- subtype description

now I like to join those tables. For example I got the product of a single
door (there are other doors which are double doors. This product belongs to
subtype single doors, which than belongs to the subcategory doors and
category historic building material out of wood.

My aim is to have a hyperlink which shows me the categorys if click on it it
shows me the subcategorys and than the subtype and than the products which
belong to all this.
So if I now create another table
called for example
table Ids
- productID
- categoryID
- subcatID
- subtypeID
will I be able to join those together and get all I want to achive building
it like this? Or do I have to many tables to join together?
Also the Id's make up my product code say for example
category b.m.o of wood makes number 10 (20, 30, 40 for others) subcategoryid
will be 1 for doors (2,3,4 there after) subtype also 1 (2,3,4) and than the
products will be 1, 2 , 3 etc.
My logic doesn't let me think of any other way. So if anyone has a good
suggestion on how to go about this please let me know.

Thank you so much if you find the time to help me out here.

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