Let's do this without soft references:

  
my %Categories;
while (<>)
{
    my( $category, $item ) = split /\t/, $_, 2;
    push @{$Categories{$category}}, $item;
}

print "$_\n" for sort @{$Categories{'dairy'}};
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Prints:

eggs
milk
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If you must have the arrays as separate variables (not just as values in the %Categories hash), you could define

%Categories = (
    fruit => \@fruit,
    meat  => \@meat,
    dairy => \@dairy,
);
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