Let k be an algebraically closed field, n >= 1 an integer, tau a k-linear Hom-finite (n + 2)-angulated category with n-suspension functor Sigma(n), a Serre functor S, and split idempotents. Let T be a basic n-rigid object and Gamma the endomorphism algebra of T. We introduce the notion of relative n-rigid objects, i.e. Sigma T-n-rigid objects of T. Then we show that the basic maximal Sigma T-n-rigid objects in T are in bijection with basic maximal tau n-rigid pairs of Gamma-modules when every indecomposable object in T is n-rigid. As an application, we recover a result in Jacobsen-Jorgensen [Maximal tau d-rigid pairs, J. Algebra 546 (2020) 119-134].
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