Eugenio Landi

Back to main page

Model Categories and Abstract Homotopy Theory

Program

The course will be an introduction to the theory of model categories and abstract homotopy theory. After the basic definitions (model structures, homotopy categories, Quillen functors) we will study homotopy limits and colimits, some useful properties of model categories and their relation to (∞,1)-categories. Time permitting we will talk about operads and the homotopy transfer theorem.

Schedule

March, Tuesday 3, 10, 17, 24, 31, from 9:00 to 11:00, in Room F of the Department of Mathematics "Guido Castelnuovo".

Lectures can be also attended remotely following this link.

Lecture Links Topics Covered Lecture Notes
Lecture 1 Part 1  |  Part 2
  • Localization of Categories
  • Definition of Model Categories
  • Ken Brown Lemma
Lecture 1
Lecture 2 Part 1  |  Part 2
  • Cylinder and Path Objects and Homotopies
  • Homotopy Categories and related results
Lecture 2
Lecture 3 Part 1  |  Part 2
  • The Quillen Model Structure on Top and SSet
  • Quillen Adjunctions and Equivalences
Lecture 3