Make a menu visible for a single category and it’s content

In order to display any specific conditional content on a single post based on it’s category, you have to edit the template called single.php.
e.g. put something like this in single.php

if ( in_category( 'category1' )) {
    //code for category1
} elseif ( in_category( array( 'category2', 'category3' ) )) {
    // code for when t
} else {
    // code for others
}