Custom Taxonomy added, still showing the category - wordpress

Question

I have made a new plugin for my WordPress site, which has the capability of creating a new post type called products and on this plug in I have added a custom taxonomy called product types. Everything is fine but my Wordpress admin panel custom post type 'product' still showing the categories option, which I don't want. That's my plug in code,
<?php function FLChildTheme_custom_post_type (){
$labels = array(
'name' => 'Products',
'singular_name' => 'products',
'add_new' => 'Add Products',
'all_items' => 'All items',
'add_new_item' => 'Add item',
'edit_item' => 'Edit Item',
'new_item' => 'New Item',
'view_item' => 'View Products',
'search_item' => 'Search Product',
'not_found' => 'No Products Found',
'not_found_in_trash' => 'No product in trash',
'parent_item_colon' => 'Parent Item',
);
$args = array(
'labels' => $labels,
'public' => true,
'has_archive' => true,
'publicly_queryable' => true,
'query_var' => true,
'rewrite' => true,
'capability_type' => 'post',
'hierarchical' => false,
'supports' => array(
'title',
'editor',
'excerpt',
'thumbnail',
'revisions',
),
'taxonomies' => array('category','post_tag'),
'menu_position' => 5,
'exclude_from_search' => false,
);
register_post_type('products', $args);
}
add_action ('init', 'FLChildTheme_custom_post_type');
/* Custom post type End*/
/* Add custom taxonomies */
function FLChildTheme_add_custom_taxonomies() {
// Add new "Locations" taxonomy to Posts
register_taxonomy('Producttypes', 'products', array(
// Hierarchical taxonomy (like categories)
'hierarchical' => true,
// This array of options controls the labels displayed in the WordPress Admin UI
'labels' => array(
'name' => _x( 'Product Types', 'taxonomy general name' ),
'singular_name' => _x( 'Product Type', 'taxonomy singular name' ),
'search_items' => __( 'Search Product Types' ),
'all_items' => __( 'All Product Types' ),
'parent_item' => __( 'Parent Product Types' ),
'parent_item_colon' => __( 'Parent Product Types:' ),
'edit_item' => __( 'Edit Product Types' ),
'update_item' => __( 'Update Product Types' ),
'add_new_item' => __( 'Add New Product Types' ),
'new_item_name' => __( 'New Product Type Name' ),
'menu_name' => __( 'Product Types' ),
),
// Control the slugs used for this taxonomy
'rewrite' => array(
'slug' => 'Producttypes', // This controls the base slug that will display before each term
'with_front' => false, // Don't display the category base before "/locations/"
'hierarchical' => true // This will allow URL's like "/locations/boston/cambridge/"
),
));
}
add_action( 'init', 'FLChildTheme_add_custom_taxonomies', 0 );
?>