Student AG Seminar: Six Functor Formalisms

When studying geometry, one is naturally led to embrace cohomology in its various incarnations. The functoriality properties of cohomology in these different settings can be uniformly encoded into the framework of abstract six functor formalisms. The advantage of abstraction is that it leads to more streamlined proofs of the various properties of cohomology in different settings (especially useful in this modern industry of constructing 'designer' cohomology theories). I will explain how the yoga of 6 functor formalism works and how to construct them in practice.