use another variable name for inner query:
like $sth2, $sth_inner, etc.

$sth = $dbh->prepare("SELECT id,name FROM category WHERE parent IS NUL
+L");
 $sth->execute or die $dbh->errstr;

 while ( @slog = $sth->fetchrow_array ) {

    $sth2 = $dbh->prepare("SELECT id,name FROM category WHERE parent =
+ '$slog[0]'");
    $sth2->execute or die $dbh->errstr;
...
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