Adding Categories across posts, and custom post types

I currently have a list of categories that go with my ‘posts’
I want the same categories to go with my custom post types ‘services’ and ‘work’

The following code, adds the tags and categories to the work and services custom posts.

add_action('init', 'demo_add_default_boxes');

function demo_add_default_boxes() {
    register_taxonomy_for_object_type('category', 'work');
    register_taxonomy_for_object_type('post_tag', 'work');
    register_taxonomy_for_object_type('category', 'services');
    register_taxonomy_for_object_type('post_tag', 'services');
}

But when I categorise a work/service post, it does not appear on the /category/ page, only the ‘posts’ from that category appear.

By default, only post_type post is shown on category pages. To enable your custom post types, you could hook pre_get_posts, check if it’s a category page, and if so add your post types:

function wpse_category_set_post_types( $query ){
    if( $query->is_category() && $query->is_main_query() ){
        $query->set( 'post_type', array( 'post', 'work', 'services' ) );
    }
}
add_action( 'pre_get_posts', 'wpse_category_set_post_types' );