Sonlu gruplarda 2-iz formülleri

This dissertation surveys 2-representations of a finite group and their 2-characters introduced by N. Ganter and M. M. Kapranov. Namely, the major aim of our thesis is to extend "trace formula" type identities to the 2-categorical setting. Thus, our main task is to compute the trace of the 2-functor R(F) in two different ways, where R is a 2-representation of a finite group G in the 2-category 2Vect_k defined by M. M. Kapranov and V. A. Voevodsky and F is a test 2-functor. Here, the finite group G is embodied in the 2-category Disc(Omega^(-1) G) and k is assumed to be the complex number field as we are not dealing with the modular representation theory. First, we review Arthur trace formula in several classical cases, such as Poisson summation formula. Next, we reprove Arthur trace formula for finite group and examine it via concrete examples as a side goal. As we are focusing on finite groups, we are using GAP, which is a system for computational discrete algebra, for explicit calculations about the trace formula. As an intermediate step, all material needed in this thesis are categorified and Tannaka duality for finite groups, which explains the connection between a finite group and its representations, is proved. Finally, a 2-category 2FinSet is defined for the test functor F and explicit computations of 2-trace formula for Z_3 and S_3 are given.