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

plugin_or_theme_functions.php

<?php
/*
 * filter pattern: manage_{taxonomy}_custom_column
 * 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_carousel_category_custom_column', 'wptc_carousel_category_column_content', 10, 3 );
function wptc_carousel_category_column_content( $content, $column_name, $term_id ) {
	// get the term object
	$term = get_term( $term_id, 'carousel_category' );

	// check if column is our custom column 'carousel_shortcode' 
	if ( 'carousel_shortcode' == $column_name ) {
		$shortcode = '<code>[wptc_carousel_slider category="'.$term->slug.'"]</code>';
		$content = $shortcode;
	}

	return $content;
}