I believe it depends. A lot of the time, it's about your partner as much as you. That is, if you're a man with a female long-term partner (say, a wife), she might object to your close friendship with another female just as much as she would object to a more traditional romantic relationship that involves sex.
Then, for her, you might be cheating, or emotionally cheating. Either way, you would have passed her boundaries. For her, you wouldn't be mono the way she understands it.
Incidentally, I think it's a shame people in mono relationship don't have as much incentive to communicate. With poly, you're kind of forced to do it at one point or another, but too many mono relationships just assume each on their own, and then get upset when the other party doesn't follow unspoken agreements (that were never there in the first place in their mind).
People seem to have that romantic notion that if you really love each other you'll have the same ideas about everything and therefore don't need to talk about them, especially if it's an "ugly" subject such as money or other partners. But it seems to me real intimacy is when you can discuss these things openly, and deal with the differences of opinion when they come up.