Flush category on post with W3 Total Cache

I have W3 Total Cache installed and working, except that it does not correctly flush my category pages on posting or updating a post. I would like to do this automatically.

Within my WordPress theme I have several category pages and they are titled category-green-widgets, category-blue-widgets etc.

Some, eg category-widgets, can pull in category-red-widgets AND category-blue-widgets (I coded it this way). I need to dump all of the categories because of this, not just the ones the post belongs to.

As a start, I’m thinking this code might work to get the post’s categories:

  /* Flush category pages */
    function category_cache_flush_on_post( $post_id ) {
        if(function_exists('w3tc_pgcache_flush_post')){
                $post_categories = wp_get_post_categories( $post_id );
                foreach($post_categories as $c)
            w3tc_pgcache_flush_post($c[0]);
        }

    }
    add_filter( 'save_post', 'category_cache_flush_on_post', 10, 1 );

So how do I dump the cache for ALL of the categories on updating or posting? What is the W3TC call for that?