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19244701 Higher Algebra II

Winter Term 2021/2022

Lecturer: Dr. Gabriel Angelini-Knoll, Prof. Dr. Holger Reich

Time and place:

  • Lecture: Thursday, 2pm--4pm, online.
  • Final Exam/homework:  oral exam -- individual dates.

Prerequisites: We assume familiarity with basic concepts from topology and homotopy theory. We assume basic concepts from homotopy theory and some familiarity with infinity categories (quasicategories) as developed for example in Rezk's lecture notes "Introduction to quasicategories" and layed out in the lecture Higher Algebra from the summer semester.

Course Overview

Recent advances in stable homotopy theory and algebraic geometry use the language of higher category theory. The lecture will give an introduction to the theory of stable infinity-categories and the generalization of classical algebra to these contexts, as developed by Jacob Lurie. This course builds on the theory of infinity-categories developed in the course Higher Algebra.


  • Jacob Lurie: Higher Topos Theory. Annals of Mathematics Studies 170, Princeton University Press 2009
  • Jacob Lurie: Higher Algebra; available from the authors homepage
  • Charles Rezk: Introduction to quasicategories; available at the authors homepage