This solution uses a hash of arrays (HoA) instead of symbolic references.

my %hoa;

while (<>)
{
    chomp;
    my( $category, $item ) = split /\t/;
    push @{$hoa{$category}}, $item;
}

for my $cat ( sort keys %hoa )
{
    print "The following are in category $cat:\n";
    for ( @{$hoa{$cat}} )
    {
        print "\t$_\n";
    }
}
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Originally posted as a Categorized Answer.