Categoricity for transfinite extensions of modules

Abstract

For each deconstructible class of modules D \mathcal D , we prove that the categoricity of D \mathcal D in a big cardinal is equivalent to its categoricity in a tail of cardinals. We also prove Shelah’s Categoricity Conjecture for ( D , ⪯ ) (\mathcal D, \preceq ) , where ( D , ⪯ ) (\mathcal D, \preceq ) is any abstract elementary class of roots of Ext.