In Schulman's 2008 paper 'Set Theory for Category Theory', he includes amongst the axioms of NBG the axiom of limitation of size. Being well known to imply the axiom of global choice, it seems to me that since ZFC+I doesn't imply global choice, this should be inconsistent with his later remark that ZFC+I has a model of NBG given by $V_{\kappa}$ for the sets, and Def$\hspace{0.1em}(V_{\kappa})$ for the proper classes. I'm sure there is something here I don't quite understand, I would greatly appreciate some clarification.