Adding fields to category manager. Does a method exist to get the link to the category edit screen?

The function which is used internally (since 3.1) is get_edit_term_link( $term_id, $taxonomy, $object_type="" ). Source view here.

There’s also a function called edit_term_link that will format the link output for you.

The built-in functions are probably better to use, because they check for user capabilities, etc., and are better for future compatability. That said, I think you’re safe using the hardcoded url for backwards compatability. I don’t know how it was done in previous versions, and I think those links might have been hardcoded like you’re doing…

Edit: I was curious what was done before that function was introduced, so I looked through the source. Prior to 3.1, get_edit_tag_link( $tag_id, $taxonomy = 'post_tag' ) did the same thing – now it’s just rewritten to use get_edit_term_link internally. So if you want to support all recent versions of WordPress, use this function:

//add the filter in order to add custom columns to the category manager 
add_filter('manage_category_custom_column', 'display_cat_columns', 10, 3);

//This function outputs the custom category image onto each row of the category manager grid.
function display_cat_columns($arg1, $column_name, $cat_id){
  if ('ce4_cat_image' == $column_name) {
      if (function_exists ('edit_term_link'))
        return edit_term_link( get_category_thumbnail_admin($cat_id, 'thumbnail'),
                '', '', $cat_id, false );
      else return '<a href="'.get_edit_tag_link($cat_id, 'category').'">'.
                get_category_thumbnail_admin($cat_id, 'thumbnail').'</a>';
  }
}