custom post types – Basic CPT Question About Categories

Missing something basic here. Here’s my CPT code…

// Create a custom post type
//
add_action( 'init', 'custom_post_type_func' );
function custom_post_type_func() {
    //posttypename = PDSH Posts
    $labels = array (
    'name' => _x( 'PDSH Posts', 'pdsh_posts' ),
    'singular_name' => _x( 'PDSH Post', 'pdsh_posts' ),
    'add_new' => _x( 'Add New', 'pdsh_posts' ),
    'add_new_item' => _x( 'Add New PDSH Post', 'pdsh_posts' ),
    'edit_item' => _x( 'Edit PDSH Post', 'pdsh_posts' ),
    'new_item' => _x( 'New PDSH Post', 'pdsh_posts' ),
    'view_item' => _x( 'View PDSH Post', 'pdsh_posts' ),
    'search_items' => _x( 'Search PDSH Posts', 'pdsh_posts' ),
    'not_found' => _x( 'No PDSH Posts found', 'pdsh_posts' ),
    'not_found_in_trash' => _x( 'No PDSH Posts found in Trash', 'pdsh_posts' ),
    'parent_item_colon' => _x( 'Parent PDSH Post:', 'pdsh_posts' ),
    'menu_name' => _x( 'PDSH Posts', 'pdsh_posts' ),
    );
    $args = array (
    'labels' => $labels,
    'hierarchical' => true,
    'description' => 'Hi, this is my custom post type.',
    'supports' => array( 'title', 'editor', 'excerpt', 'author', 'thumbnail', 'trackbacks', 'custom-fields', 'comments', 'revisions', 'page-attributes' ),
    'taxonomies' => array( 'category', 'post_tag', 'page-category' ),
    'public' => true,
    'show_ui' => true,
    'show_in_menu' => true,
    'show_in_nav_menus' => true,
    'publicly_queryable' => true,
    'exclude_from_search' => false,
    'has_archive' => true,
    'query_var' => true,
    'can_export' => true,
    'rewrite' => true,
    'capability_type' => 'post'
    );
    register_post_type( 'pdsh_posts', $args );
}

Works great!
I’m using the WP All Import plugin to create 3378 PDSH Posts with three parent categories: Alphabetical, Creators, Morality. They all look correctly populated here…
enter image description here
BUt when I view one of those categories the archive page can’t see the posts, goes to content-none, throws up a Not Found.
Do I need to register all 107 categories somehow, or maybe just the three parent categories?