In Shulman's 2008 paper '[Set Theory for Category Theory](https://arxiv.org/abs/0810.1279)', he includes amongst the axioms of $\sf NBG$ the axiom of *limitation of size*. Being well known to imply the axiom of global choice, it seems to me that since $\sf ZFC+I$ doesn't imply global choice, this should be inconsistent with his later remark that $\sf ZFC+I$ has a model of $\sf NBG$ 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.