NMAA06020U  Categories and Topology (CatTop)

Volume 2017/2018

MSc Programme in Mathematics


Topics in algebraic topology centered around the use of categories in homotopy theory and simplicial methods. Topics include simplicial sets, nerves of categories, classifying spaces, algebraic K-theory of exact categories, homotopy (co)limits, localization and completion.



Learning Outcome
  • Knowledge: To display knowledge of the course topics and content, at the level of a beginning researcher.
  • Skills: To be able to use the acquired knowledge to perform computations.
  • Competencies: To be able to produce independent proofs in extension of   
    the acquired knowledge.
AlgTopI and HomAlg or similar. Knowledge of AlgTop1.5 and AlgTopII will be advantageous.
4 hours lectures and 3 hours exercises per week for 9 weeks.
7,5 ECTS
Type of assessment
Continuous assessment
Weekly exercises. The weekly assignments are scored equally,
and the sum of the homework scores has to correspond to a passing
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner

30 minutes oral exam without preparation time. No aids allowed. Several internal examiners

Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome.

  • Category
  • Hours
  • Lectures
  • 36
  • Theory exercises
  • 27
  • Preparation
  • 143
  • Total
  • 206