Filter links to WP categories to a page with the same name.

link_categories_to_related_page.php

<?php

/**
 * Changes link to a WP category to a static page with the same name.
 * For, you know, whatever.
 */
function link_categories_to_related_page($categoryUrl, $categoryId) {
    $category = get_category($categoryId);
    if ($relatedPage = get_page_by_title($category->name)) {
        $categoryUrl = get_permalink($relatedPage->ID);
    }
    return $categoryUrl;
}

add_filter('category_link', 'link_categories_to_related_page', 10, 2);