  Suppose a spacetime $M$ is a quotient of a spacetime $V$ by a discrete group
of isometries. It is shown how causality conditions in the two spacetimes are
related, and how can one learn about the future causal boundary on $M$ by
studying structures in $V$. The relations between the two are particularly
simple (the boundary of the quotient is the quotient of the boundary) if both
$V$ and $M$ have spacelike future boundaries and if it is known that the
quotient of the future completion of $V$ is past-distinguishing. (That last
assumption is automatic in the case of $M$ being multi-warped.)
