This course will be an introduction to higher category theory focussing on the approach via infinity-categories.
Lecture notes (until Jan 08).
Problem Set 1 (due Oct 23)
Problem Set 2 (due Oct 30)
Problem Set 3 (due Nov 06)
Problem Set 4 (due Nov 13)
Problem Set 5 (due Nov 20)
Problem Set 6 (due Nov 27)
Problem Set 7 (due Dec 04)
Problem Set 8 (due Dec 11)
Problem Set 9 (due Dec 18)
Problem Set 10 (due Jan 8)
Problem Set 11 (due Jan 15)
Problem Set 12 (due Jan 22)
Problem Set 13 (due Jan 29)
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 infinity 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.
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.
Oral exam. Admission requirement: Submit solutions to 50% of the homework problems.