I have two tables, a Department and a Category, both only have 3 fields.
Id (PK),
Name,
Description.
These two tables join together in a 1 to many, Department to Category, and that is where my question is.
Should I create a 3rd table with 3 fields, Id, Department_Id, Category_Id, for joining the 2 tables together. This keeps Category from having duplicate records if it is in more than 1 department.
Or
Add a Department_Id into Category table, and have it have multiple category records if it is in more than one department?
It sounds as if it's many to many rather than 1 to many.
In that case, you must use a 3rd table. But that table should NOT have a separate id column. The key for that table should be ( department_id, category_id ) or ( category_id, department_id ), the order depending on how you use / lookup the data.