Can I use the [product_categories] shortcode within a custom widget

1. Create a custom widget by extending the `WP_Widget` class and adding the necessary code to display the categories using the `[product_categories]` shortcode.

2. In the `widget()` function of your custom widget class, you can use the `do_shortcode()` function to execute the `[product_categories]` shortcode and display the categories.

Here's an example of how you can implement this:

php
class My_Product_Categories_Widget extends WP_Widget {

    public function __construct() {
        parent::__construct(
            'my_product_categories_widget',
            __('My Product Categories', 'textdomain'),
            array( 'description' => __( 'Display product categories using a shortcode', 'textdomain' ), )
        );
    }

    public function widget( $args, $instance ) {
        echo $args['before_widget'];
        if ( ! empty( $instance['title'] ) ) {
            echo $args['before_title'] . apply_filters( 'widget_title', $instance['title'] ). $args['after_title'];
        }
        echo do_shortcode('[product_categories]');
        echo $args['after_widget'];
    }

    public function form( $instance ) {
        $title = ! empty( $instance['title'] ) ? $instance['title'] : __( 'Product Categories', 'textdomain' );
        ?>
        <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 esc_attr( $title ); ?>">
        </p>
        <?php
    }

    public function update( $new_instance, $old_instance ) {
        $instance = array();
        $instance['title'] = ( ! empty( $new_instance['title'] ) ) ? strip_tags( $new_instance['title'] ) : '';
        return $instance;
    }

}

// Register the widget
function register_my_product_categories_widget() {
    register_widget( 'My_Product_Categories_Widget' );
}
add_action( 'widgets_init', 'register_my_product_categories_widget' );

In this example, we create a custom widget called `My_Product_Categories_Widget` that extends the `WP_Widget` class. In the `widget()` function, we use `do_shortcode()` to execute the `[product_categories]` shortcode and display the categories.

You can customize the widget further by adding options to allow users to specify attributes for the `[product_categories]` shortcode, such as `number`, `orderby`, or `hide_empty`.

After registering the widget using `register_widget()` and `widgets_init` action, you can add the custom widget to your sidebar or other widget areas in WordPress.