/**
 * Add image for category
 */
add_action('init', 'my_category_module');
function my_category_module()
{
    $taxonomy = 'category';
    add_action($taxonomy . '_add_form_fields', 'add_custom_field_for_taxonomy');
    add_action($taxonomy . '_edit_form_fields', 'add_custom_field_for_taxonomy');
    add_action('create_' . $taxonomy, 'save_custom_field_for_taxonomy');
    add_action('edited_' . $taxonomy, 'save_custom_field_for_taxonomy');
}

function add_custom_field_for_taxonomy($tag)
{
    $category_images = get_option('category_images');
    $category_image = '';
    if (is_array($category_images) && array_key_exists($tag->term_id, $category_images)) {
        $category_image = $category_images[$tag->term_id];
    }
    echo '<tr><th scope="row" valign="top"><label for="auteur_revue_image">Image</label></th><td>';
    
    if ($category_image != '') {
        echo '<img src=" ' . $category_image . '"/>';
    }
    echo '<input type="text" name="category_image" id="category_image" size="40" value="' . $category_image . '"/><p class="description">Image url.</p></td></tr>';
}

function save_custom_field_for_taxonomy($term_id)
{
    if (isset($_POST['category_image'])) {
        $category_images = get_option('category_images');
        $category_images[$term_id] =  $_POST['category_image'];
        update_option('category_images', $category_images);
    }
}

$category_images = get_option('category_images');
if (isset($category_images[$term_id]) && $category_images[$term_id]) {
    echo '<img class="img" src="' . $category_images[$term_id] . '"/>';
}