Extending Walker_Category Class

class Walker_Simple_Example extends Walker_Category {

/**
	         * What the class handles.
	         *
	         * @see Walker::$tree_type
	         * @since 2.1.0
	         * @var string
	         */
	        public $tree_type = 'category';

	        /**
	         * Database fields to use.
	         *
	         * @see Walker::$db_fields
	         * @since 2.1.0
	         * @todo Decouple this
	         * @var array
	         */
	        public $db_fields = array ('parent' => 'parent', 'id' => 'term_id');

	        /**
	         * Starts the list before the elements are added.
	         *
	         * @see Walker::start_lvl()
	         *
	         * @since 2.1.0
	         *
	         * @param string $output Passed by reference. Used to append additional content.
	         * @param int    $depth  Depth of category. Used for tab indentation.
	         * @param array  $args   An array of arguments. Will only append content if style argument value is 'list'.
	         *                       @see wp_list_categories()
	         */
	        public function start_lvl( &$output, $depth = 0, $args = array() ) {
	                if ( 'list' != $args['style'] )
	                        return;

	                $indent = str_repeat("\t", $depth);
	                $output .= "$indent<ul class='product_list'>\n";
	        }

	        /**
	         * Ends the list of after the elements are added.
	         *
	         * @see Walker::end_lvl()
	         *
	         * @since 2.1.0
	         *
	         * @param string $output Passed by reference. Used to append additional content.
	         * @param int    $depth  Depth of category. Used for tab indentation.
	         * @param array  $args   An array of arguments. Will only append content if style argument value is 'list'.
	         *                       @wsee wp_list_categories()
	         */
	        public function end_lvl( &$output, $depth = 0, $args = array() ) {
	                if ( 'list' != $args['style'] )
	                        return;

	                $indent = str_repeat("\t", $depth);
	                $output .= "$indent</ul>\n";
	        }

	        /**
	         * Start the element output.
	         *
	         * @see Walker::start_el()
	         *
	         * @since 2.1.0
	         *
	         * @param string $output   Passed by reference. Used to append additional content.
	         * @param object $category Category data object.
	         * @param int    $depth    Depth of category in reference to parents. Default 0.
	         * @param array  $args     An array of arguments. @see wp_list_categories()
	         * @param int    $id       ID of the current category.
	         */
	        public function start_el( &$output, $category, $depth = 0, $args = array(), $id = 0 ) {
	                /** This filter is documented in wp-includes/category-template.php */
	                $cat_name = apply_filters(
	                        'list_cats',
	                        esc_attr( $category->name ),
	                        $category
	                );

	                $link = '<a href="' . esc_url( get_term_link( $category ) ) . '" ';
	                if ( $args['use_desc_for_title'] && ! empty( $category->description ) ) {
	                        /**
	                         * Filter the category description for display.
	                         *
	                         * @since 1.2.0
	                         *
	                         * @param string $description Category description.
	                         * @param object $category    Category object.
	                         */
	                        $link .= 'title="' . esc_attr( strip_tags( apply_filters( 'category_description', $category->description, $category ) ) ) . '"';
	                }

	                $link .= '>';
	                $link .= $cat_name . '</a>';

	                if ( ! empty( $args['feed_image'] ) || ! empty( $args['feed'] ) ) {
	                        $link .= ' ';

	                        if ( empty( $args['feed_image'] ) ) {
	                                $link .= '(';
	                        }

	                        $link .= '<a href="' . esc_url( get_term_feed_link( $category->term_id, $category->taxonomy, $args['feed_type'] ) ) . '"';

	                        if ( empty( $args['feed'] ) ) {
	                                $alt = ' alt="' . sprintf(__( 'Feed for all posts filed under %s' ), $cat_name ) . '"';
	                        } else {
	                                $alt = ' alt="' . $args['feed'] . '"';
	                                $name = $args['feed'];
	                                $link .= empty( $args['title'] ) ? '' : $args['title'];
	                        }

	                        $link .= '>';

	                        if ( empty( $args['feed_image'] ) ) {
	                                $link .= $name;
	                        } else {
	                                $link .= "<img src='" . $args['feed_image'] . "'$alt" . ' />';
	                        }
	                        $link .= '</a>';

	                        if ( empty( $args['feed_image'] ) ) {
	                                $link .= ')';
	                        }
	                }

	                if ( ! empty( $args['show_count'] ) ) {
	                        $link .= ' (' . number_format_i18n( $category->count ) . ')';
	                }
	                if ( 'list' == $args['style'] ) {
	                        $output .= "\t<li";
	                        $class = 'cat-item product-post cat-item-' . $category->term_id;
	                        if ( ! empty( $args['current_category'] ) ) {
	                                $_current_category = get_term( $args['current_category'], $category->taxonomy );
	                                if ( $category->term_id == $args['current_category'] ) {
	                                        $class .=  ' current-cat';
	                                } elseif ( $category->term_id == $_current_category->parent ) {
	                                        $class .=  ' current-cat-parent';
	                                }
	                        }
	                        $output .=  ' class="' . $class . '"';
	                        $output .= ">$link\n";
	                }

					if (function_exists('z_taxonomy_image_url')) echo z_taxonomy_image_url();

					else {
	                        $output .= "\t$link<br />\n";
	                }
	        }

	        /**
	         * Ends the element output, if needed.
	         *
	         * @see Walker::end_el()
	         *
	         * @since 2.1.0
	         *
	         * @param string $output Passed by reference. Used to append additional content.
	         * @param object $page   Not used.
	         * @param int    $depth  Depth of category. Not used.
	         * @param array  $args   An array of arguments. Only uses 'list' for whether should append to output. @see wp_list_categories()
	         */
	        public function end_el( &$output, $page, $depth = 0, $args = array() ) {
	                if ( 'list' != $args['style'] )
	                        return;

	                $output .= "</li>\n";
	        }

	}