Introduction to higher category theory

Lectures: Tu,Fr 10:15 - 11:45
Instructor: Tobias Dyckerhoff
Office: Geomatikum 338
Email: tobias.dyckerhoffATuni-hamburg de

Tutorials: Tu 14:15 - 15:45
Tutor: Tobias Dyckerhoff

About

This course will be an introduction to higher category theory focussing on the approach via ∞-categories.

Topics

Review of ordinary category theory
Simplicial sets and simplicial homotopy theory
The basic language of ∞-categories
Simplicial categories and quasi-categories
Stable ∞-categories

The main reference will be Lurie's book "Higher topos theory". More specifically, we will begin by describing the rudimentary features of the theory of ∞-categories, and then move on to a more systematic study via model categories, comparison results with other models, limits and colimits, applications in the context of derived categories, and more.

Literature

Brandenburg: Einführung in die Kategorientheorie
Mac Lane: Categories for the working mathematician
Weibel: An introduction to homological algebra
Goerss-Jardine: Simplicial Homotopy Theory
Lurie: Higher topos theory
Lurie: Higher Algebra
Joyal-Tierney: Quasi-categories vs Segal spaces
This list will be updated as the course progresses.

Prerequisites

Familiarity with basic concepts from category theory and algebraic topology will be useful, but we will review those aspects that are relevant for this course.

Final Exam