If we have numbers $a,b$, they are called summands of $a+b$ or factors of $a\cdot b$. Given two modules $M,N$, they are direct summands of $M\oplus N$.
Likewise, given two sets $A,B$, they can be called factors of $A\times B$. What word describes the relationship between sets $A,B$ and $A\cup B$ or $A\sqcup B$?
