Deconstructible abstract elementary classes of modules and categoricity

Abstract We prove a version of Shelah's categoricity conjecture for arbitrary deconstructible classes of modules. Moreover, we show that if is a deconstructible class of modules that fits in an abstract elementary class such that (1) is closed under direct summands and (2) refines direct summands, then is closed under arbitrary direct limits. In the Appendix, we prove that the assumption (2) is not needed in some models of ZFC.