Definitions of cohabitation agreement
a legal agreement between two people living together but who are not married to each other, especially as partners for life, usually in a sexual relationship. A cohabitation agreement may help when applying for a mortgage and other official matters where it is important for a third party to understand that the relationship is stable, serious, and intended to be permanent.
We have a cohabitation agreement, so if we did ever break up then we are both clear on who owns what.