Achim Krause and Thomas Nikolaus: Higher Algebra

23rd November, 2020

This is a 13-lecture course, with each lecture being about 60-90 minutes or so, given in person by Achim Krause and Thomas Nikolaus. It gives an introduction to higher category theory, ∞-categories, spectra, and so on.

  1. Achim Krause: ∞-categories
  2. Thomas Nikolaus: Limits
  3. Thomas Nikolaus: Colimits
  4. Achim Krause: Derived categories as ∞-categories
  5. Achim Krause: Slices and filtered colimits
  6. Thomas Nikolaus: Derived functors
  7. Thomas Nikolaus: Non-abelian derived functors
  8. Achim Krause: Spectra
  9. Thomas Nikolaus: Symmetric monoidal ∞-categories
  10. Thomas Nikolaus: En-algebras
  11. Thomas Nikolaus: p-adic completion
  12. Thomas Nikolaus: The Tate construction
  13. Achim Krause: The Tate diagonal

These videos were produced by the University of Münster, in particular the homotopy theory group there.