Topology Seminar: Injective and projective model structures on enriched diagram categories

K. Hess, M. Kedziorek, E. Riehl, and B. Shipley have developed methods to induce model structures from an adjunction which they apply to prove the existence of injective and projective model structures on categories of diagrams in accessible model categories. In this talk, I will explain how to adapt their proof to an enriched setting, in order to prove the existence of injective and projective model structures on some enriched diagram categories. I will talk in particular about the case of enriched diagrams from a small simplicial category to the category of pointed simplicial sets, and then generalize it by replacing the category of pointed simplicial sets by other symmetric monoidal categories, which are locally presentable bases and accessible model categories.