I think it looks pretty good. Your use of DBI, its shortcut methods (selectall_arrayref and fetchall_arrayref), and the Slice options is spot-on: this is exactly why these methods are there.

I only have some stylistic comments, prompted by the fact that add_subject_loop modifies one of its arguments.

1. I would try to remove the side-effects, and make it a proper function
2. I would try to move the sql strings and the preparation of the subject handle out of get_category_loop

I believe that would improve the structure of your program, and increase its maintainability. Abstracting away the lower-level sql stuff is a good idea. See for instance Perl Hacks for some pointers.

I'm also a big fan of prepare_cached, since it can remove the need of global $sth variables.

Here's a suggested refactoring:

sub get_category_loop {

    return [
        map { 
            $_->{subject_loop} 
                = get_subject_loop( delete $_->{category_id} ); # dele
+te returns the value that was in the hash
            $_
        }
        @{ $dbh->selectall_arrayref(sql_category(), {Slice => {}}) }
    ];

}

sub get_subject_loop {

    my $category_id = shift;

    my $sth = $dbh->prepare_cached( sql_subject() );
    $sth->execute($category_id);
    return $sth->fetchall_arrayref({});

}

sub sql_category {

    return q{
        SELECT   category_id,
                 category_name
        FROM     category
        ORDER BY category_id
    };

}

sub sql_subject {

    return q{
        SELECT   subject_id,
                 subject_name
        FROM     subject
        WHERE    category_id = ?
        ORDER BY subject_name
    };

}
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I'm not so sure anymore if the map is justified. I feel a foreach loop would probably be easier to read now.