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On Perfectly Generating Projective Classes in Triangulated Categories
Authors:George Ciprian Modoi
Affiliation:1. Faculty of Mathematics and Computer Science, Chair of Algebra , “Babe?-Bolyai” University , Cluj-Napoca, Romania cmodoi@math.ubbcluj.ro
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.
Keywords:Brown representability  Perfect projective class  Triangulated category with coproducts
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