Set a them for all subset of category

There are two functions you need to accomplish this. First, you will have to know whether a category is a subactegory of 16. This is cat_is_ancestor_of. Second, you will have to force that category to use the template of 16, which you do with locate_template. Knowing this, you can build a filter on the function that determines which template to use for a category page like this:

add_filter ('category_template', 'wpse24089_category_template');

function wpse24089_category_template( $template ) {
    $current_cat = get_queried_object_id();
    if (cat_is_ancestor_of (16, $current_cat))
        $template = locate_template( 'category-slider.php' );
    return $template;
    }