Conducted in
term:
2023L
Erasmus code: 11.1
ISCED code: 0541
ECTS credits:
6
Language:
English
Organized by:
Faculty of Mathematics, Informatics, and Mechanics
Related to study programmes:
Model Categories 1000-1M23KMO
- Weak factorization systems, the small object argument, model categories, cofibrantly generated model categories.
- Homotopies, homotopy equivalences, the homotopy category, Quillen functors and Quillen equivalences.
- The model structure on the category of topological spaces.
- The Kan–Quillen model structure on the category of simplicial sets.
- Model structures on the category of chain complexes.
- Projective and injective model structures on categories of diagrams, homotopy limits and colimits.
- Reedy model structures, mapping spaces in model categories.
Type of course
elective monographs
Requirements
Prerequisites
Prerequisites (description)
Familiarity with basics of topology within the scope of the Topology I course. Understanding of the fundamental notions of homotopy theory (homotopy equivalence, fundamental group, chain complexes and singular homology) as discussed in Topology II. It will be helpful to have experience with category theory as in the course Elements of Category Theory. Understanding of concepts of the Algebraic Topology course such as singular cohomology, CW-complexes and homotopy groups is also recommended.
Course coordinators
Learning outcomes
- Familiarity with basic concepts of abstract homotopy theory in the framework of model categories: homotopies, homotopy equivalences, fibrant and cofibrant replacements.
- Ability to recognize homotopy non-invariant constructions and to approximate them by homotopy invariant ones using Quillen functors.
- Understanding of the classical homotopy theory of topological spaces as a special case of abstract homotopy theory in model categories.
- Familiarity with the current developments in abstract homotopy theory sufficient for taking up independent research.
Assessment criteria
Participation in classes, written homework assignments and oral exam.
Bibliography
- Mark Hovey Model Categories 1999
- Philip Hirschhorn Model Categories and Their Localizations 2002
- William Dwyer, Jan Spaliński Homotopy theories and model categories (Handbook of Algebraic Topology 1995)
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: