子カテゴリを非表示に

default-widgets.phpの533行目当たりから始まる部分が
カテゴリ一覧ウィジェットを生成する部分みたいです。

/**
* Categories widget class
*
* @since 2.8.0
*/
class WP_Widget_Categories extends WP_Widget {
public function __construct() {
$widget_ops = array('classname' => 'widget_categories', 'description' => __( "A list or dropdown of categories." ) );
parent::__construct('categories', __('Categories'), $widget_ops);
}
public function widget( $args, $instance ) {
/** This filter is documented in wp-includes/default-widgets.php */
$title = apply_filters( 'widget_title', empty( $instance['title'] ) ? __( 'Categories' ) : $instance['title'], $instance, $this->id_base );
$c = ! empty( $instance['count'] ) ? '1' : '0';
$h = ! empty( $instance['hierarchical'] ) ? '1' : '0';
$d = ! empty( $instance['dropdown'] ) ? '1' : '0';
echo $args['before_widget'];
if ( $title ) {
echo $args['before_title'] . $title . $args['after_title'];
}
$cat_args = array( 'orderby' => 'name', 'show_count' => $c, 'hierarchical' => $h);
if ( $d ) {
$cat_args['show_option_none'] = __('Select Category');
/**
* Filter the arguments for the Categories widget drop-down.
*
* @since 2.8.0
*
* @see wp_dropdown_categories()
*
* @param array $cat_args An array of Categories widget drop-down arguments.
*/
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 home_url(); ?>/?cat="+dropdown.options[dropdown.selectedIndex].value;
		}
	}
	dropdown.onchange = onCatChange;
/* ]]> */
</script>
<?php
} else {
?>
<div id="right_categories">
<ul>
<?php
$cat_args['title_li'] = '';
/**
		 * Filter the arguments for the Categories widget.
		 *
		 * @since 2.8.0
		 *
		 * @param array $cat_args An array of Categories widget options.
		 */
wp_list_categories( apply_filters( 'widget_categories_args', $cat_args ) );
?>
</ul>
</div>
<?php
}
echo $args['after_widget'];
}
public function update( $new_instance, $old_instance ) {
$instance = $old_instance;
$instance['title'] = strip_tags($new_instance['title']);
$instance['count'] = !empty($new_instance['count']) ? 1 : 0;
$instance['hierarchical'] = !empty($new_instance['hierarchical']) ? 1 : 0;
$instance['dropdown'] = !empty($new_instance['dropdown']) ? 1 : 0;
return $instance;
}
public 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( 'Display 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
}
}

559行目からの部分がカテゴリ一覧を抽出する部分の様で、ここに depth という引数を記入します。 depth => 1　が’第一階層のみを表示’のようです。なので

$cat_args = array('depth' => '1', 'orderby' => 'name', 'show_count' => $c, 'hierarchical' => $h);

で親カテゴリだけが表示されます。