That’s how I would interpret it, too, but I don’t think that’s a necessary component of monogamy, despite being the way that many people practice it. Someone could say “I want to be in a monogamous relationship with you if you want to be in one with me,” i.e. the desire for monogamy should be reciprocal rather than forced. A romantic relationship is, ideally, a mutual agreement.
That’s how I would interpret it, too, but I don’t think that’s a necessary component of monogamy, despite being the way that many people practice it. Someone could say “I want to be in a monogamous relationship with you if you want to be in one with me,” i.e. the desire for monogamy should be reciprocal rather than forced. A romantic relationship is, ideally, a mutual agreement.