Homotopical algebra

Masters course – Spring 2018


Prof. Kathryn Hess Bellwald


Aras Ergus







This course will provide an introduction to model category theory, which is an abstract framework for generalizing homotopy theory beyond topological spaces and continuous maps. We will study numerous examples of model categories and their applications in algebra and topology.




Lecture: Monday, 8h15 – 10h
Exercises: Thursday, 10h15 -12h
Rooms: MA 30 (lecture), MA 31 (exercises)



0. Homotopy theory of topological spaces

1. Category theory

2. Model categories and their homotopy categories

3. Transfer theorems





  • W.G. Dwyer and J. Spalinski, Homotopy theories and model categories, Handbook of Algebraic Topology, Elsevier, 1995, 73-126. (Article no. 75 here)


  • P.G. Goerss and J.F. Jardine, Simplicial Homotopy Theory, Progress in Mathematics 174, Birkhäuser Verlag, 1999.


  • M. Hovey, Model Categories, Mathematical Surveys and Monographs 63, American Mathematical Society, 1999.



NB: A more detailed bibliography can be found in the syllabus file above.


Link to Aras’s solution sketches (requires GASPAR login).