Bahran, Cihan2016-01-082016-01-082012http://hdl.handle.net/11693/15472Ankara : The Department of Mathematics and the Graduate School of Engineering and Science of Bilkent University, 2012.Thesis (Master's) -- Bilkent University, 2012.Includes bibliographical references leaves 101-102.Representations of EI-categories occur naturally in algebraic K-theory and algebraic topology (see [4], [10], [12]). In this thesis, we study EI-category representations with finite projective dimension. We apply this general theory to orbit 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, the constant functor over the orbit category of a finite group G with respect to the family 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 constant functor over the orbit category of all subgroups with prime power order and with integral coefficients never has a finite projective resolution unless G itself has prime power order.vii, 102 leavesEnglishinfo:eu-repo/semantics/openAccessEI-categoriesprojective dimensionconstant functororbit categoriesRim’s theoremQA169 .B34 2012Categories (Mathematics)Functor theory.Algebraic functions.Projective spaces.K-theory.Thesis