turkmath.org

Categorification is a recent area of mathematics aiming to enrich set-based theories with category-based ones. There are some famous examples of categorification from last century, such as categorification of the Euler characteristic by homology theories. The area has attracted a lot of attention after the categorification of the famous knot invariant by Khovanov in 1999. Since then, many interesting objects have been categorified, including quantum groups and Hecke algebras. We will make a gentle introduction to the ideas and techniques used in categorification. Since sets are foundations of all of todays mathematics, the aim is to encourage each participant to think of ways to categorify their favorite object in mathematics.