The GD > Single Taxonomies block ([gd_single_taxonomies]) shows a listing’s categories and tags on the details page. Its options cover most changes without code:

• Taxonomy: categories and tags (default), categories only (cats) or tags only (tags).
• Limit: the most terms to show.
• Prefix: the taxonomy name such as “Place Category:” (default), icons, or none (0).

So this shows the categories only, with no label in front:

[gd_single_taxonomies taxonomy="cats" prefix="0"]

Show only the main category with its parents

Every listing has a default category, the main one used for its map icon and similar things. GD > Single Taxonomies lists categories in alphabetical order, so limit="1" gives you the first one alphabetically, which may not be the default.

To show just the default category, with its parent categories before it, add this snippet. It creates a [my_gd_default_category] shortcode you can place in the details page template.

add_shortcode( 'my_gd_default_category', 'my_gd_default_category_output' );
function my_gd_default_category_output() {
	global $gd_post;

	if ( empty( $gd_post->default_category ) ) {
		return '';
	}

	$taxonomy = $gd_post->post_type . 'category';
	$term_id  = (int) $gd_post->default_category;
	$term_ids = array_reverse( get_ancestors( $term_id, $taxonomy, 'taxonomy' ) );
	$term_ids[] = $term_id;

	$links = array();
	foreach ( $term_ids as $id ) {
		$term = get_term( $id, $taxonomy );
		if ( $term && ! is_wp_error( $term ) ) {
			$links[] = '<a href="' . esc_url( get_term_link( $term ) ) . '">' . esc_html( $term->name ) . '</a>';
		}
	}

	return '<div class="my-gd-default-category">' . implode( ' / ', $links ) . '</div>';
}

Add it with the Code Snippets plugin. For finer changes to the block’s own output, the geodir_details_taxonomies_output filter receives the HTML for each taxonomy before it is shown. All the block options are in GD > Single Taxonomies.