How to hide {{ entry.title }} on a {structure} page but show it on a {structure}/{category-slug} page
Figured it out. 

    {% set categories = craft.categories.group('fellowsCat') %}

 &lt;ul&gt;
  {% nav category in craft.categories
    .group('fellowsCat')
    %}
    &lt;li&gt;
      &lt;a href="{{ category.url }}"&gt;{{ category.title }}&lt;/a&gt;
      {% ifchildren %}
        &lt;ul&gt;
          {% children %}
        &lt;/ul&gt;
      {% endifchildren %}
    &lt;/li&gt;
  {% endnav %}
&lt;/ul&gt; 

&lt;ul&gt;


{# --- this is the key line here ---#}
{% if category is defined %}

{% set entries = craft.entries({
  relatedTo:  category,

})
%}

{% if craft.entries.relatedTo(category) %} 


      {% for entry in entries %}
        &lt;li&gt;  &lt;a href="{{ entry.url }}"&gt;{{ entry.title }}&lt;/a&gt;&lt;/li&gt;
      {% endfor %}
      &lt;/ul&gt;

     {% else %} 
    nothing to see
     {% endif %} 
     {% endif %}