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401-3180-20L 4 Credits BSC , MSC D-MATH

Introduction to Homotopy Theory and Model Category Structure

Lecturers & Examiners: Dr. Julien Ducoulombier
Number of participants limited to 24.
VVZ CR n/a

Last Updated: 2026-02-05 15:41:20

Abstract

Introductory seminar about category theory and techniques in Algebraic topology such as model category structure and "homotopy" limits and colimits.

Objective

It is well known that topological spaces are endowed with a homotopy theory classifying objects up to continuous deformations. Model categories provide a natural setting for homotopy theory and it has been used in some parts of algebraic K-theory, algebraic geometry and algebraic topology, where homotopy-theoretic approaches led to deep results. The goal of this seminar is to get an introduction to model structures through examples (topological spaces, simplicial sets, chains complexes...). To get further into this theory, we develop the notion of derived functors with applications to homotopy limits and colimits.

Resources

Literature

"Homotopy theories and model categories" Dwyer and Spalinski "A primer on homotopy colimits" Dugger "Model categories" Hovey

General Information

Language
English
Levels
BSC , MSC

Examination

Type
ungraded semester performance
Participants are expected to attend the seminar, give a presentation and write a report.

Registration & Places

Limited places (Special selection)
Signup Start
06.01.2020
Signup End
12.02.2020
Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
seminar Introduction to Homotopy Theory and Model Category Structure
  • Tue 13:15-15:00 (CHN D 46)
2 h weekly

Offered In

  • Mathematics Bachelor
    • Seminars (This semester, many seminars have a waiting list with special selection procedure. If no other criteria apply, a definitive registration will be granted first of all to students who haven't got another seminar registration. Here is the best procedure for dealing with two waiting lists: first choose your preferred seminar and afterwards choose an alternative seminar.)
  • Mathematics Master
    • Seminars and Semester Papers
      • Seminars (This semester, many seminars have a waiting list with special selection procedure. If no other criteria apply, a definitive registration will be granted first of all to students who haven't got another seminar registration. Here is the best procedure for dealing with two waiting lists: first choose your preferred seminar and afterwards choose an alternative seminar.)