Follow the link I gave you to figure out which template file is used to display your category archives:
WP works like this: will be looking first for #1, if it doesn't find then looks for #2 etc.
So, let's say you have only an archive.php file - you need to edit that one.
WARNING: your edits will affect the way how other views are displayed, too, e.g. by editing the archive.php your monthly archives and archives of other categories will also be displayed in the way you edited the template file.
If you want only the category archive view to be customized > cretae a category.php file (by saving the archive.php as category.php) and edit the new file:
- remove the_content tag from the Loop
- leave only template tags you want to be displayed (example: the_title, the_date or the_time etc.)