Filter existing hook using parameter and foreach loop

Question

I am trying to create a filter to add a custom column to the edit page of any custom category that might exist in Wordpress. I am aware that the filter hook must be in the form, manage_edit-{$cat}_columns. Lets say that this is the function to add:

/* Add custom column to lists */
function add_shortlink_column( $columns ) {
    return array_merge( $columns, 
        array( 'shortlink' => __( 'Shortlink', 'your_text_domain' ) ) );
} 

Because I want to cover ALL custom categories (current or future) I must do this using a foreach loop after calling get_taxonomies.

However add_filter is causing me problems...

Suppose that I have only two categories; topics and product_cat.

If I try this everything works fine and the column is added:

$value1 = 'topics';
$value2 = 'product_cat';
$filters = array( "manage_edit-{$value1}_columns", "manage_edit-{$value2}_columns" );
foreach ( $filters as $filter ) {
    add_filter( $filter, 'add_shortlink_column' );
}

However, if I try this it does not work.

$args = array(
  'public'   => true,
  '_builtin' => false     
); 
$taxonomies = get_taxonomies( $args, 'names', 'and' );  
foreach($taxonomies as $key => $taxonomy) {
    $filter = "manage_edit-{$taxonomy}_columns";
    add_filter( $filter, 'add_shortlink_column' );      
}

I am pretty sure that this is some sort of syntax problem. But I cannot figure it out. Any help would be much appreciated.

Thanks

Answer 1

As per the suggestion of Milo who pointed me to the right direction, this problem has now been resolved.

All I had to do was this...

add_action( 'init', 'get_custom_tax' );
function get_custom_tax() {
  $args = array(
    'public'   => true,
    '_builtin' => false   
  ); 
  $taxonomies = get_taxonomies( $args, 'names', 'and' );    
  foreach($taxonomies as $key => $taxonomy) {
      $filter = "manage_edit-{$taxonomy}_columns";
      add_filter( $filter, 'add_shortlink_column', 50, 1 );     
  } 
}