EI-kategorileri üzerinde projektif çözücüler

Representations of EI-categories occur naturally in algebraic K-theory and algebraictopology (see [4], [10], [12]). In this thesis, we study EI-category representationswith finite projective dimension. We apply this general theory toorbit categories of finite groups and prove Rim's theorem for the orbit category(Theorem B in [5]). It follows from this theorem that, for a fixed prime p, theconstant functor over the orbit category of a finite group G with respect to thefamily of p-subgroups and with coefficients in Z(p) has finite projective dimension,which we denote by pd(G, p). In this thesis, we calculate pd(S4, 2) and pd(S5, 2)explicitly, which are among the first nontrivial cases. We also prove that the constantfunctor over the orbit category of all subgroups with prime power order andwith integral coefficients never has a finite projective resolution unless G itselfhas prime power order.