in_category outside the loop

I’m setting up a second sidebar where I put the “submenus” of my site.

Could you expand on what you are trying to achieve.

Resource:
in_category()

vs.

is_category()

For use in sidebar, if category archive show chidren

<?php
if (is_category( )) {
  $cat = get_query_var('cat');
  $parent = get_category ($cat);
  if ($parent->parent) {
    wp_list_categories ('child_of=' . $parent->parent);
    } else {
    wp_list_categories ('child_of=' . $cat);
  }
}
?>

For use in sidebar, display only top level Pages, but when viewing a Page that has children (or is a child) show only children of that parent
When visiting main page, all top level pages are listed in the sidebar.
When click on a top level page with no children, all top level pages are listed.
When click on a top level page with children, just the children pages are listed.
When click on a children page, just the children of that parent are listed.

<?php
$output = wp_list_pages('echo=0&depth=1&title_li=<h2>Top Level Pages </h2>' );
if (is_page( )) {
  $page = get_query_var('page_id');
  if ($post->post_parent) {
    $page = $post->post_parent;
  }
  $children=wp_list_pages( 'echo=0&child_of=' . $page . '&title_li=' );
  if ($children) {
    $output = wp_list_pages ('echo=0&child_of=' . $page . '&title_li=<h2>Child Pages</h2>');
  }
}
echo $output;
?>