特定のカテゴリに属するタグ一覧を表示させたい

色々と検索していたら、このコードを見つけました。

ほぼほぼやりたいことはできたのですが、
ここから任意の件数分表示したい場合どのようにしたらいいでしょうか？

<?php

function nestmenu( $args ) {

    $nestmenu = '';

    if ( ! isset( $args['exclude'] ) ) {
        $args['exclude'] = '';
    }

    $opt = array(
        'hide_empty'   => true,
        'exclude_tree' => $args['exclude']
    );

    $cat_array = get_categories( $opt );

    $nestmenu  = "<div id='nestmenu'>\n";
    $nestmenu .= "<ul class='nestmenu-category'>\n";

    foreach ( $cat_array as $key => $cat ) {

        $cat_name = $cat->name;
        $cat_num = $cat->count;
        $cat_link = get_category_link( $cat->term_id );
        $tag_array = nestmenu_relation($cat->term_id);

        $nestmenu .= "<li><h2><a href='$cat_link' title='$cat_name'>$cat_name ($cat_num)</a></h2></li>\n";
        $nestmenu .= "<ul class='nestmenu-tag'>\n";

        foreach ( $tag_array as $tags ) {

            foreach ( $tags as $tag ) {

                $tag_link = esc_url( home_url( '/' ) . '?cat=' . $cat->term_id . '&tag=' . $tag['slug'] );
                $nestmenu .= "<li><a href='$tag_link' title='$tag[name]'>$tag[name] ($tag[count])</a></li>";

            }

        }

        $nestmenu .= "</ul>\n";

    }

    $nestmenu .= "</ul>\n";
    $nestmenu .= "</div>\n";

    return $nestmenu;

}
add_shortcode( 'nestmenu', 'nestmenu' );
add_filter( 'widget_text', 'do_shortcode' );

function nestmenu_relation( $term_id = false ) {

    if ( $term_id === false ) {
        return $term_ids;
    }

    $taxonomy = get_terms(
        array(
            'category',
            'post_tag'
        ),
        array(
            'hide_empty' => true,
            'include'    => $term_id
        )
    );

    $taxonomy = $taxonomy[0]->taxonomy;

    if ( ! is_null( $taxonomy ) ) {

        $args = array(
            'nopaging'            => 1,
            'ignore_sticky_posts' => 1,
            'order'               => 'ASK',
            'tax_query'           => array(
                array(
                    'taxonomy' => $taxonomy,
                    'terms'    => $term_id,
                    'field'    => 'id',
                    'operator' => 'AND'
                 )
            )
        );

        $my_query = new WP_Query( $args );

        if( $my_query->have_posts() ) {

            if ( $taxonomy === 'category' ) {
                $taxonomy = 'post_tag';
            } else {
                $taxonomy = 'category';
            }

            while ( $my_query->have_posts() ) : $my_query->the_post();

                $term = get_the_terms( get_the_ID(), $taxonomy );

                if ( $term ) {

                    foreach ( $term as $value ) {

                        if ( ! isset( $term_ids['term'][$value->term_id] ) ) {

                            $term_info = array(
                                'id'   => $value->term_id,
                                'name' => $value->name,
                                'slug' => $value->slug,
                            );

                            $term_ids['term'][$value->term_id] = $term_info;

                        }

                        $term_ids['term'][$value->term_id]['count'] += 1;

                    }

                }

            endwhile;

            wp_reset_query();

        }

        if ( $term_ids['term'] ) {

            $term_ids['term'] = array_merge( $term_ids['term'] );

            foreach ( $term_ids['term'] as $key => $value ) {
                $key_id[$key] = $value['count'];
            }
            array_multisort( $key_id, SORT_DESC, $term_ids['term'] );

        }

    }

    return $term_ids;
}

?>