Homotopical Algebra

A.Y. 2021/2022
6
Max ECTS
42
Overall hours
SSD
MAT/02
Language
English
Learning objectives
The main task of this course is to give an introduction to the methods of homotopical algebra.
Expected learning outcomes
Knowledge of the fundamentals of the abstract homotopy theory and applications.
Course syllabus and organization

Single session

Responsible
Lesson period
Second semester
More specific information on the delivery modes of training activities for academic year 2021/22 will be provided over the coming months, based on the evolution of the public health situation.
Course syllabus
Homotopy & homology. Weak equivalences & quasi isomorphisms. Fibrations & cofibrations. Model categories & homotopy categories. Quillen functors, derived functors & equivalences. Simplicial homotopy & geometric realisation. Universal homotopy & universal homology.
Prerequisites for admission
We assume known the basic notions from category theory, algebraic topology & homological algebra.
Teaching methods
Lectures.
Teaching Resources
Jardine's Lectures on Homotopy Theory available online.
M. Hovey: Model Categories, Math Surveys & Monographs Vol. 63 AMS, 1999.
W.G. Dwyer & J. Spalinski: Homotopy theories and model categories in Handbook of Algebraic Topology I.M. James (ed.) North-Holland, 1995.
Assessment methods and Criteria
Some homework will be assigned during the lectures. Preferably, the solutions shall be provided within the end of the course. Next a seminar on your favorite subject will be assigned according to the themes hinted in class.
MAT/02 - ALGEBRA - University credits: 6
Lessons: 42 hours
Educational website(s)
Professor(s)
Reception:
Wednesday h. 2-4 p.m. or email contact
Zoom Meeting