#!/usr/bin/perl

use strict;
use warnings;

my $file = '/path/to/file.txt';
my %hash;

{
    #Abschnitstrenner auf "\n\n", siehe perldoc perlvar
    local $/ = "\n\n";
    open my $fh, '<', $file or die $!;
    while( my $entry = <$fh> ){
        my @cats = $entry =~ /(cat=\d+)/g;
        my ($id) = $entry =~ /(ID=[^,;]+)/;
        next unless $id;
        push @{ $hash{$id} }, @cats;
    }
}

for my $key ( keys %hash ){
    print $key, " - " , join(" : ", @{ $hash{$key} }),"\n";
}