In Shulman's 2008 paper '[Set Theory for Category Theory](https://arxiv.org/abs/0810.1279)', 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 $\operatorname{Def}(V_{\kappa})$ for the proper classes. I'm sure there is something here I don't quite understand, I would greatly appreciate some clarification.