1. Target the menu like you would normally do with the MMenu WordPress plugin.
  2. Ensure your category listing on the page looks like this:
    <nav id="main-menu">
    <ul><?php wp_list_cats();?></ul>
    </nav>
  3. Now for the final part, add this to your functions.php file so the MMenu active class can be implemented in the category layout.
    add_filter( 'wp_list_categories', function( $html ) {
     return str_replace( ' current-cat', ' current-menu-item', $html );
    });