Abstract: Higher category theory is an emerging area of modern mathematics with applications to areas as diverse as algebraic geometry and theoretical computer science. However, there are multiple proposed foundations for this subject. Jacob Lurie believes that higher category theory should be founded on the theory of quasi-categories, which are studied using the Joyal model structure on simplicial sets. On the other hand, Carlos Simpson believes that higher category theory should be founded on simplicial presheaves. This talk will be the beginnings of trying to reconcile these two views, by developing a model structure for simplicial presheaves on a topological space where the weak equivalences are maps which are Joyal weak equivalences on stalks.