Generic Departments

Would we cap the titles of departments in supermarkets? I believe that both the department's specific name and the word department itself should be lowercased, as in seafood department.

Hence, all examples below (both words) should be lowercased, correct?

•Alesia works in the Seafood Department.
•David works part-time in the Meat Department.
•Sal was promoted to manager of the Deli Department.

Thanks.