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
Oral exam. Admission requirement: Submit solutions to 50% of the homework problems.