Adding child fields to a parent record

I have a Vendor Table (Vendor Name, Address, Phone, etc).
I also have a Material Category Table (Wire, Cable, Fittings)

The Vendor table is a parent to the Material Category Table ( a vendor can have many material categories)


In the Vendor form there's an embedded report that shows all of the material categories that have been assigned to the vendor.

I'd like a way to search the Vendor table for the particular category. Is there a way for the parent table to look down to the child for the categories, and have that field be searchable on the parent table?


I'd like the users to be able to enter "wire" on the Vendor Table search report, and get a list of vendors with the wire category assigned to it.