Pre-Seminar: Derivators are a powerful, but not too complicated enhancement of triangulated categories that in particular gives us a functorial cone construction. We discuss basic results surrounding strong stable derivators (which give rise to triangulated categories) and also symmetric monoidal strong stable derivators (giving rise to tensor triangulated categories a la Balmer).
Seminar: We will give a construction for the "affine line" over a derivator which mimics the construction of an affine line over a scheme. We detail the associated structure/evaluation morphisms, monoidal structure, and a "universal property" of this affine line. Though our motivation comes from algebraic geometry, since derivators are not limited to this context we expect that the notion of affine line will have relevance in fields such as modular representation theory or stable/equivariant homotopy theory if we use the framework of derivators. Joint work with Paul Balmer.
Host: Paul Smith