Categories and Topology (CatTop)

Course content

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, homotopy (co)limits, localization and completion.




MSc Programme in Mathematics

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.

4 hours lectures and 4 hours exercises per week for 9 weeks.

In previous years lecture notes were used. It will be aimed to make these notes available from Absalon and/or the lecturers homepage.

Knowledge of foundational algebraic topology corresponding to roughly Chapter 1-5 in Hatcher's book "Algebraic Topology" is assumed (e.g., obtained thorough the UCPH courses AlgTop, HomAlg and AlgTopII).

Academic qualifications equivalent to a BSc degree is recommended.

Continuous feedback during the course of the semester
7,5 ECTS
Type of assessment
Continuous assessment
Written exercises, handed in weekly, whose totality will determine the final grade.
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner
Criteria for exam assessment

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

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 36
  • Preparation
  • 134
  • Theory exercises
  • 36
  • English
  • 206