Tannaka duality

Content / Literature / Recommended previous knowledge The aim of this course is to give a modern treatment of the theory of Tannaka duality in algebraic geometry. To keep the prerequisites low, I will start by introducing the necessary categorical background: symmetric monoidal categories, enriched categories, some basic two-dimensional category theory, (co)monads, descent, and Beck's theorem. Using this, I will then discuss the basic theory of Tannaka duality, including generalizations from working over a ground field to an arbitrary commutative ring. The necessary background on Hopf algebroids and stacks will be developed along the way.