Representation Theory in Verona

Reading Course on Higher Categories

Wednesday, 10:00-12:00, Sala Riunioni II floor

The course is devoted to the concept of an infinity category. In the first session, Rosanna Laking will guide us through the video of an introductory lecture by Emily Riehl. Next, we will review the notion of a model category and discuss some motivating examples from algebraic topology. Then we will read some chapters of the book "Higher Categories and Homotopical Algebra" by Denis-Charles Cisinski. Finally, there will be a lecture series delivered by Gustavo Jasso from the University of Bonn.

Start: Wednesday, November 13.


November 13th:   Introduction (Rosanna Laking, video of a lecture by Emily Riehl)
November 20th:   Model Categories, part 1 (Tsutomu Nakamura)
November 27th:   Model Categories, part 2 (Francesco Sentieri)
December 4th (9:30-11:30): Model Categories, part 3
December 9th:    The Fundamental Groupoid (Sofia Franchini/Giulia Cavicchioni)
December 11th:   Geometric and Combinatorial Simplicies (Sofia Franchini/Giulia Cavicchioni)
January 8th:         The category of simplicial sets and the nerve of a category (Lidia Angeleri)
January 15th:       ∞-categories (Cao Weiqing)
January 29th:       Kan-Quillen and Joyal model structures (Rosanna Laking)
February 5th:       Fibrations and opfibrations (Lorenzo Martini)
February 12th:     The Grothendieck construction (Rosie Laking)

Lecture Series by Gustavo Jasso, University of Bonn:

Tuesday, February 18, 10:00-12:00
Wednesday, February 19, 11:00-12:00
Thursday, February 20, 10:00-12:00

February 18, and Friday, February 21, 14:00-16:00: Discussion

Allen HatcherAlgebraic Topology, Cambridge University Press 2002   
Denis-Charles CisinskiHigher Categories and Homotopical Algebra, Cambridge University Press 2019 
Michael Barr, Charles Wells  Category Theory for Computing Science, Chapter 12  pdf
Emily Riehl, The model-independent theory of (∞,1)-categories  (lectures at Isaac Newton Institute for Mathematical Sciences 2018; video available on