wait- are you looking to display the full content of the first post on the category page and then follow that w/ the normal excerpts? that is a different animal and would involve overriding the category loop like i originally thought, but with a counter. then you test for the counter being equal to 1, and for that post show the full content (the_content() ) in place of thematic_content which shows excerpts on archive pages by default.
the category loop is shown in content-extensions.php in the thematic/library/extensions folder. copy the thematic_category_loop function into your child's functions.php and rename it childtheme_override_category_loop()
if this is not the case and you are still doing what i was thinking above (though now that i think on it, won't you end up w/ the full post of something immediately followed by the excerpt for the same post?
so while i don't think this what you're actually after anymore, it will show you how to get the category id .you don't have to shout- just know how to talk wordpress... which actually a quick google of 'get category id' or something similar reveals.
$category = get_the_category();
$cat_id = $category->cat_ID ;
$args = array('show_posts'=>1,'category'=>$cat_id);
$myposts = get_posts($args);
foreach( $myposts as $post ) : setup_postdata($post); //from the get_posts codex