Category or Page templates?

Hi,

Basically, I have 5 categories for different posts and I made a page
http://www.domain.com/page to display navigation to categories in a list as here:

<ul>
<?php
    $categories=  get_categories('hide_empty=0');
  foreach ($categories as $cat) {
    echo '<li>'.'<a href="'.get_category_link($cat->cat_ID).'">'.$cat->description.'</a>'.'</li>';

  }
 ?>
</ul>

I now want to be able to click on the category link so that it would take me to

http://www.domain.com/page/cat-1 and not http://www.domain.com/categories/cat-1

how can I do that? Is there a way to create a page template and then apply a category filter depending on the category selected on http://www.domain.com/page?