%0 Journal Article
%T On perfectly generating projective classes in triangulated categories
%A George Ciprian Modoi
%J Mathematics
%D 2008
%I arXiv
%R 10.1080/00927870902911789
%X We say that a projective class in a triangulated category with coproducts is perfect if the corresponding ideal is closed under coproducts of maps. We study perfect projective classes and the associated phantom and cellular towers. Given a perfect generating projective class, we show that every object is isomorphic to the homotopy colimit of a cellular tower associated to that object. Using this result and the Neeman's Freyd--style representability theorem we give a new proof of Brown Representability Theorem.
%U http://arxiv.org/abs/0811.0404v2