Writer's Block: There Can Be Only One
Monogamy can mean many different things. If monogamy means that the person you are with is the only person that you can be with, and you both agree, then that is monogamy.
If you are in a couple and agree that it is okay to be with other people, so long as you both agree to that, then it is not cheating. One can have a monogamous relationship and still have sex with other people.
Taken further, if you both believe that it is okay to fall in love with other people, we come to polyamory. As long as both (or all!) of the people involved believe that it is okay to live and love that way, then it is not cheating.
If you are in a couple and agree that it is okay to be with other people, so long as you both agree to that, then it is not cheating. One can have a monogamous relationship and still have sex with other people.
Taken further, if you both believe that it is okay to fall in love with other people, we come to polyamory. As long as both (or all!) of the people involved believe that it is okay to live and love that way, then it is not cheating.