code

<?php

        //for this category on an archive page, get the ID
        $thisID = get_query_var('cat');

        $get_children_cats = array(
            'child_of' => $thisID //get children of this parent using the thisID variable from earlier
        );

//firstly, load data for your child category
$child = get_category($thisID);

//from your child category, grab parent ID
$parent = $child->parent;

//load object for parent category
$parent_name = get_category($parent);

//grab a category name
$parent_name = $parent_name->name;

            echo '<strong><a href=" ' . get_category_link( $parent ) . ' ">' . $parent_name . '</a></strong><p>';

        $child_cats = get_categories( $get_children_cats );//get children of this parent category

        foreach( $child_cats as $child_cat ){
            //for each child category, get the ID
            $childID = $child_cat->cat_ID;

            echo '<strong> - <a href=" ' . get_category_link( $childID ) . ' ">' . $child_cat->name . '</a></strong>';
        } //end of categories logic


?><p>
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