Monogamous
Monogamous or monogamy is a form of relationship (or purely sexual partnership) where two people are exclusively in a relationship with one another. This type of relationship is typically romantically and sexually exclusive, though people in a monogamous relationship do not have to be married or living with each other (sometimes referred to as nesting partners). Friendship and other more casual non-sexual or non-romantic connections with other people are not necessarily excluded, but people may agree to limit casual connections with people who are the same gender as a monogamous person's partner. Having a romantic or sexual relationship with someone other than one's monogamous partner that violates the agreement made with that partner is referred to as infidelity or cheating.
Non-Monogamy and Open Relationships
There are people who identify as monogamous but have agreements within their relationship to be "open". This could mean that they are open to engage in sexual connections with other people. This may be limited by agreed upon restrictions, such as only being allowed to engage with other partners when their monogamous partner is present (swingers). These agreements are often considered to be part of ethical non-monogamy, although many people who engage in this still consider themselves to be essentially monogamous.
There are also cases where people in a monogamous relationship will engage with others outside of the connection with their partner and their knowledge. This could be an agreement that is often called "don't ask, don't tell", where their partner gives consent but doesn't want to hear about any activities or relationships. However in most cases this would be considered "cheating".
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