If G is a finite group, then the usual version of the Green correspondence applies to finitely generated kG-modules when k is a field of characteristic p > 0 or a p-adic ring. The paper presents a categorical version of the Green correspondence and a version of the Burry–Carlson–Puig theorem that remain valid for arbitrary modules and coefficient rings. In this generality, however, it is not clear whether the Green correspondent of a finitely generated module is always finitely generated.