The goal of this talk is to show that there is a robust algebraic theory for categories, where for example, rings are replaced by monoidal categories. We will introduce the category of presentable infinity categories, and show how one can endow it with the Lurie tensor product. This is a robust construction, which in particular comes equipped with a good theory of algebras and modules. A particular case of interest will be that every presentable infinity category comes equipped with a canonical module structure over the category of spaces, and explain how one can use this to make sense of tensoring an algebra by a circle. Speaker(s): Attilio Castano (University of Michigan)