I don't think the way you have done it is wrong, but the way you have done is does not make it scalable and you are likely to run into problems if the system needs expanding. I.e: products in more than one category; changing the products category.
I suggest you make a new table called categories and give each category a name and an ID and indicate weather a category is a sub category of another category. You can then add a field to your products table called category ID.
Code:
# categories
category_id INTEGER
category_name VARCHAR(50)
parent_id INTEGER DEFAULT 0