<div class="prev-product"><?php previous_post_link('%link','prev'); ?> </div>
<div class="next-product"><?php next_post_link( '%link','next'); ?>

<div class="prev-product"><?php previous_post_link('%link','prev', TRUE); ?> </div>
<div class="next-product"><?php next_post_link( '%link','next', TRUE); ?></div>

function save_product_cat(){
global $post;
    $terms = get_the_terms( $post->ID, 'product_cat' );
    wp_set_post_categories( $post->ID, $terms );
    wp_set_object_terms( $post->ID, $terms->slug, 'category');
}

add_action('save_post', 'save_product_cat');