Homological Algebra


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Module Leader: Pavel Safronov

This course provides an introduction to homological algebra. We will discuss both theoretical background (abelian and derived categories, dg categories) as well as practical tools (group cohomology, spectral sequences).

Lectures [Mondays, 10:00-11:30]

  • Lecture 1: Introduction to abelian categories.
  • Lecture 2: Abelian categories continued.
  • Lecture 3: Injective and projective objects.
  • Lecture 4: Derived functors and sheaf cohomology.
  • Lecture 5: Group cohomology and Hochschild cohomology.
  • Lecture 6: Spectral sequences.
  • Lecture 7: Introduction to derived categories.
  • Lecture 8: Derived categories continued.
  • Lecture 9: dg categories and dg enhancements.
  • Lecture 10: Simplicial objects, Dold--Kan correspondence.