You need to go inside the code of your category.php and…
Change:
the_content(); //or similer
to:
the_excerpt();
Goog luck..
Revised Answer for twenty eleven theme:
1. Open content.php and search for this line:
<?php if ( is_search() ) : // Only display Excerpts for Search ?>
2. change it to this:
<?php if ( is_search() || is_category() || is_archive() ) : // Only display Excerpts for Search ?>
Hope this helps..
Best regards, Sagive.