Introductory Workshop: Noncommutative Algebraic Geometry: "How to enhance categories, and why"

February 6, 2024
  • Noncommutative geometry
  • derived categories
  • Derived Algebraic Geometry
  • Infinity Categories
  • Deformation Theory
  • Categorical Resolutions
  • noncommutative resolutions
It has become accepted wisdom by now that when you localize a category with respect to a class of morphisms, what you get is not just a category but a category "with a homotopical enhancement". Typically, the latter is made precise through the machinery of "infinity-categories", or "quasicategories", but this is quite heavy technically and not really optimal from the conceptual point of view. I am going to sketch an alternative technique based on Grothendieck's idea of a "derivator".