Using an include file?

I’d like to create files that can be edited within the admin. These files will be included in their respective categories inside header.php.

For example, for cat4, I’ll have cat4header.php. Using a conditional in header.php, the contents of cat4header.php will display at the top of every post in category 4. When cat4header.php doesn’t have any contents, nothing displays and no space in taken up.

How can this be done?