On perfectly generating projective classes in triangulated categories

Abstract

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.

to appear in Comm. Algebra

Cited by in corpus (2)

• The dual of the homotopy category of projective modules satisfies Brown representability
• The dual of Brown representability for some derived categories