  An antiferromagnetic insulator (AFI) bearing a compensated interface to an
adjacent conventional superconductor (S) has recently been predicted to
generate N\'eel triplet Cooper pairs, whose amplitude alternates sign in space.
Here, we theoretically demonstrate that such N\'eel triplets enable control of
the superconducting critical temperature in an S layer via the angle between
the N\'eel vectors of two enclosing AFI layers. This angle dependence changes
sign with the number of S monolayers providing a distinct signature of the
N\'eel triplets. Furthermore, we show that the latter mediate a similarly
distinct exchange interaction between the two AFIs' N\'eel vectors.
