I have a products table that contains a FK for a category, the Categories table is created in a way that each category can have a parent category, example:
Compu
The best solution for this is at the database design stage. Your categories table needs to be a Nested Set. The article Managing Hierarchical Data in MySQL is not that MySQL specific (despite the title), and gives a great overview of the different methods of storing a hierarchy in a database table.
So based on your example, if your hierarchy table was a nested set your query would look something like this:
SELECT * FROM products
INNER JOIN categories ON categories.id = products.category_id
WHERE categories.lft > 2 and categories.rgt < 11
the 2 and 11 are the left and right respectively of the Processors
record.