Update post title with category name after editing a category

Question

I have this relationshop between some categories and posts where the name of the category is also the name of the post. When I add a new category, a post that has the same title as the category is created. Now when I edit one of those category titles, I want the corresponding post to update its title automatically as well. Here's what I have:

function update_group($post_id) {

    // get the category object
    $category = get_term_by( 'id', $post_id, 'category');

    // use the object to get your values
    $name = $category->name;

    $updates = array(
        'ID' => 996,
        'post_title' => $name
    );

    wp_update_post($updates);

}

add_filter('edit_category' , 'update_group' );

The problem with this simple code is that when I fetch the category name, the new name that I submitted has not been saved yet when edit_category runs, so the first time I edit a category, wp_update_post updates the post with the old name. That means the post will only get the new and correct name when I submit the category change again via the admin page. Is there a way around this? How do I get the sumbitted category name the first time edit_category is executed?