How do I match categories?

I ask you to tell me.
What if the file looks like this? How to correctly determine the category, gender and everything sotal?

<categories>
<category id="1">Mens</category>
<category id="2" parentId="1">sweaters and shirts</category>
<category id="3" parentId="2">sweaters</category>
<category id="4" parentId="1">jackets and trousers</category>
</categories>

<offer>
<categoryId>3</categoryId>
<categoryId>10</categoryId>
</offer>

I am now doing something like this:

function my_map_data( $data ) {
    $map = array(
		'3' => 'sweaters',
 );
    return ( array_key_exists( $data, $map ) ) ? $map[ $data ] : $data;
}

But something tells me that I am doing nonsense and need to compare categories differently.