Source

File: wp-includes/rest-api/endpoints/class-wp-rest-taxonomies-controller.php

public function prepare_item_for_response( $taxonomy, $request ) {
		$base = ! empty( $taxonomy->rest_base ) ? $taxonomy->rest_base : $taxonomy->name;

		$fields = $this->get_fields_for_response( $request );
		$data   = array();

		if ( in_array( 'name', $fields, true ) ) {
			$data['name'] = $taxonomy->label;
		}

		if ( in_array( 'slug', $fields, true ) ) {
			$data['slug'] = $taxonomy->name;
		}

		if ( in_array( 'capabilities', $fields, true ) ) {
			$data['capabilities'] = $taxonomy->cap;
		}

		if ( in_array( 'description', $fields, true ) ) {
			$data['description'] = $taxonomy->description;
		}

		if ( in_array( 'labels', $fields, true ) ) {
			$data['labels'] = $taxonomy->labels;
		}

		if ( in_array( 'types', $fields, true ) ) {
			$data['types'] = array_values( $taxonomy->object_type );
		}

		if ( in_array( 'show_cloud', $fields, true ) ) {
			$data['show_cloud'] = $taxonomy->show_tagcloud;
		}

		if ( in_array( 'hierarchical', $fields, true ) ) {
			$data['hierarchical'] = $taxonomy->hierarchical;
		}

		if ( in_array( 'rest_base', $fields, true ) ) {
			$data['rest_base'] = $base;
		}

		if ( in_array( 'visibility', $fields, true ) ) {
			$data['visibility'] = array(
				'public'             => (bool) $taxonomy->public,
				'publicly_queryable' => (bool) $taxonomy->publicly_queryable,
				'show_admin_column'  => (bool) $taxonomy->show_admin_column,
				'show_in_nav_menus'  => (bool) $taxonomy->show_in_nav_menus,
				'show_in_quick_edit' => (bool) $taxonomy->show_in_quick_edit,
				'show_ui'            => (bool) $taxonomy->show_ui,
			);
		}

		$context = ! empty( $request['context'] ) ? $request['context'] : 'view';
		$data    = $this->add_additional_fields_to_object( $data, $request );
		$data    = $this->filter_response_by_context( $data, $context );

		// Wrap the data in a response object.
		$response = rest_ensure_response( $data );

		$response->add_links(
			array(
				'collection'              => array(
					'href' => rest_url( sprintf( '%s/%s', $this->namespace, $this->rest_base ) ),
				),
				'https://api.w.org/items' => array(
					'href' => rest_url( sprintf( 'wp/v2/%s', $base ) ),
				),
			)
		);

		/**
		 * Filters a taxonomy returned from the REST API.
		 *
		 * Allows modification of the taxonomy data right before it is returned.
		 *
		 * @since 4.7.0
		 *
		 * @param WP_REST_Response $response The response object.
		 * @param WP_Taxonomy      $item     The original taxonomy object.
		 * @param WP_REST_Request  $request  Request used to generate the response.
		 */
		return apply_filters( 'rest_prepare_taxonomy', $response, $taxonomy, $request );
	}