401-3180-20L  Introduction to Homotopy Theory and Model Category Structure

SemesterSpring Semester 2020
LecturersJ. Ducoulombier
Periodicitynon-recurring course
Language of instructionEnglish
CommentNumber of participants limited to 24.


401-3180-20 SIntroduction to Homotopy Theory and Model Category Structure2 hrs
Tue13:15-15:00CHN D 46 »
J. Ducoulombier

Catalogue data

AbstractIntroductory seminar about category theory and techniques in Algebraic topology such as model category structure and "homotopy" limits and colimits.
ObjectiveIt 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.
Literature"Homotopy theories and model categories" Dwyer and Spalinski

"A primer on homotopy colimits" Dugger

"Model categories" Hovey
Prerequisites / NoticeThe students are expected to be familiar with topological spaces
and fundamental groups.

This seminar takes the form of a working group, where interactions are encouraged. Participants are expected to attend the seminar, give a presentation and write a report. Topic will be assigned during the first meeting.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits4 credits
ExaminersJ. Ducoulombier
Typeungraded semester performance
Language of examinationEnglish
RepetitionRepetition only possible after re-enrolling for the course unit.
Additional information on mode of examinationParticipants are expected to attend the seminar, give a presentation and write a report.

Learning materials

No public learning materials available.
Only public learning materials are listed.


No information on groups available.


PlacesLimited number of places. Special selection procedure.
Beginning of registration periodRegistration possible from 06.01.2020
PriorityRegistration for the course unit is only possible for the primary target group
Primary target groupMathematics BSc (404000) starting semester 05
Mathematics MSc (437000)
Applied Mathematics MSc (437100)
Waiting listuntil 18.02.2020
End of registration periodRegistration only possible until 12.02.2020

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