add custom column to taxonomy (carousel_category) list table page.

plugin_or_theme_functions.php

<?php
/*
 * filter pattern: manage_edit-{taxonomy}_columns
 * where {taxonomy} is the name of taxonomy e.g; 'carousel_category'
 * codex ref: https://codex.wordpress.org/Plugin_API/Filter_Reference/manage_$taxonomy_id_columns
 */
add_filter( 'manage_edit-carousel_category_columns' , 'wptc_carousel_category_columns' );
function wptc_carousel_category_columns( $columns ) {
	// remove slug column
	unset($columns['slug']);
	
	// add carousel shortcode column
	$columns['carousel_shortcode'] = __('Carousel Shortcode');

	return $columns;
}