Hide a category of posts from main blog, and only show in category view

I was able to get the result that I wanted by putting the following into the functions.php file in my theme directory:

function exclude_category( $query ) {
    if ( $query->is_home() && $query->is_main_query() ) {
        $query->set( 'cat', '-208' );
    }
}
add_action( 'pre_get_posts', 'exclude_category' );

The result of using this code was that any posts tagged with category 208 do not appear in the main blog, but they do appear in category 208 as well as in any other categories they are tagged with.

To exclude multiple categories, edit the following line of the above as follows:

$query->set( 'cat', '-208,-9,-50' );

You can find full details here.

Thanks to Milo for his comment pointing me in the right direction.