On perfectly generating projective classes in triangulated categories

Details On perfectly generating projective classes in triangulated categories On perfectly generating projective classes in triangulated categories

2008-11-03

arxiv.org/abs/0811.0404v2

Comm. Algebra, 38, 2010

Mathematics

Category Theory

to appear in Comm. Algebra

Scientific paper

10.1080/00927870902911789

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.

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