The code below is an attempt to take the WP_Widget_Categories class and use it as the basis for a custom categories widget based on the default categories widget.

I'm getting no output however and the widget is not showing up in the "Available Widgets" listing. What am I doing wrong?

<?php
/*
Plugin Name: My Categories Widget
Version: 1.0
*/


class MY_Widget_Categories extends WP_Widget {

    function MY_Widget_Categories() {
        $widget_ops = array( 'classname' => 'widget_categories', 'description' => __( "A list or dropdown of categories" ) );
        $this->WP_Widget('categories', __('Categories'), $widget_ops);
    }

    function widget( $args, $instance ) {
        extract( $args );

        $title = apply_filters('widget_title', empty( $instance['title'] ) ? __( 'Categories' ) : $instance['title']);
        $c = $instance['count'] ? '1' : '0';
        $h = $instance['hierarchical'] ? '1' : '0';
        $d = $instance['dropdown'] ? '1' : '0';

        echo $before_widget;
        if ( $title )
            echo $before_title . $title . $after_title;

        $cat_args = array('orderby' => 'name', 'show_count' => $c, 'hierarchical' => $h);

        if ( $d ) {
            $cat_args['show_option_none'] = __('Select Category');
            wp_dropdown_categories(apply_filters('widget_categories_dropdown_args', $cat_args));
?>

<script type='text/javascript'>
/* <![CDATA[ */
    var dropdown = document.getElementById("cat");
    function onCatChange() {
        if ( dropdown.options[dropdown.selectedIndex].value > 0 ) {
            location.href = "<?php echo get_option('home'); ?>/?cat="+dropdown.options[dropdown.selectedIndex].value;
        }
    }
    dropdown.onchange = onCatChange;
/* ]]> */
</script>

<?php
        } else {
?>
        <ul>
<?php
        $cat_args['title_li'] = '';
        wp_list_categories(apply_filters('widget_categories_args', $cat_args));
?>
        </ul>
<?php
        }

        echo $after_widget;
    }

    function update( $new_instance, $old_instance ) {
        $instance = $old_instance;
        $instance['title'] = strip_tags($new_instance['title']);
        $instance['count'] = $new_instance['count'] ? 1 : 0;
        $instance['hierarchical'] = $new_instance['hierarchical'] ? 1 : 0;
        $instance['dropdown'] = $new_instance['dropdown'] ? 1 : 0;

        return $instance;
    }

    function form( $instance ) {
        //Defaults
        $instance = wp_parse_args( (array) $instance, array( 'title' => '') );
        $title = esc_attr( $instance['title'] );
        $count = isset($instance['count']) ? (bool) $instance['count'] :false;
        $hierarchical = isset( $instance['hierarchical'] ) ? (bool) $instance['hierarchical'] : false;
        $dropdown = isset( $instance['dropdown'] ) ? (bool) $instance['dropdown'] : false;
?>
        <p><label for="<?php echo $this->get_field_id('title'); ?>"><?php _e( 'Title:' ); ?></label>
        <input class="widefat" id="<?php echo $this->get_field_id('title'); ?>" name="<?php echo $this->get_field_name('title'); ?>" type="text" value="<?php echo $title; ?>" /></p>

        <p><input type="checkbox" class="checkbox" id="<?php echo $this->get_field_id('dropdown'); ?>" name="<?php echo $this->get_field_name('dropdown'); ?>"<?php checked( $dropdown ); ?> />
        <label for="<?php echo $this->get_field_id('dropdown'); ?>"><?php _e( 'Show as dropdown' ); ?></label><br />

        <input type="checkbox" class="checkbox" id="<?php echo $this->get_field_id('count'); ?>" name="<?php echo $this->get_field_name('count'); ?>"<?php checked( $count ); ?> />
        <label for="<?php echo $this->get_field_id('count'); ?>"><?php _e( 'Show post counts' ); ?></label><br />

        <input type="checkbox" class="checkbox" id="<?php echo $this->get_field_id('hierarchical'); ?>" name="<?php echo $this->get_field_name('hierarchical'); ?>"<?php checked( $hierarchical ); ?> />
        <label for="<?php echo $this->get_field_id('hierarchical'); ?>"><?php _e( 'Show hierarchy' ); ?></label></p>
<?php
    }

}

function my_categories_init()
{
  register_sidebar_widget(__('My Categories Widget'), 'MY_Widget_Categories');
}

add_action("plugins_loaded", "my_categories_init");
?>