NMAA06020U Categories and Topology (CatTop)

Volume 2025/2026
Education

MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject

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 theory of chain complexes, homotopy (co)limits, localization and completion, first steps in the theory of infinity-categories.

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.
Literature

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", along a familiarity with basic homological algebra is assumed. These qualifications can e..g, be obtained through the UCPH courses AlgTop, HomAlg and AlgTopII.

Academic qualifications equivalent to a BSc degree is recommended.
4 hours lectures and 4 hours exercises per week for 9 weeks.
  • Category
  • Hours
  • Lectures
  • 36
  • Preparation
  • 134
  • Theory exercises
  • 36
  • Total
  • 206
Written
Oral
Individual
Collective
Continuous feedback during the course of the semester
Credit
7,5 ECTS
Type of assessment
Continuous assessment
Type of assessment details
Written exercises, handed in weekly, whose totality will determine the final grade.
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner
Re-exam

30 minutes oral examination with no aids or preparation time. The oral examination will cover the entire material of the course, including the exercise sets.

Criteria for exam assesment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.