Monoidal categories and graded objects - Nicolas Garrel

Talk by Nicolas Garrel (University of Antwerp), at the Antwerp Algebra, Geometry and Number Theory Seminar on November 22, 2024.
In this talk we wish to explain how to view graded objects (modules, rings, etc.) as monoidal functors defined on discrete monoidal categories (we introduce these categories and functors), and how to leverage this point of view to define non-trivial graded objects using a simple categorical set-up. We apply this in particular to the algebraic and hermitian K-theory of Azumaya algebras.