Custom Post Type API doesn’t show taxonomy or category array

The taxonomy for custom post type must be included into REST API just as the custom post itself.
Add this to your custom post taxonomy arguments array:

'show_in_rest' => true,
'rest_base'    => 'category',
'rest_controller_class' => 'WP_REST_Terms_Controller'

For more information http://v2.wp-api.org/extending/custom-content-types/

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