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Generalised Moore spectra in a triangulated category | | David Pauksztello
; | | Date: |
30 Mar 2009 | | Abstract: | In this paper we consider a construction in an arbitrary triangulated
category T which resembles the notion of a Moore spectrum in algebraic
topology. Namely, given a compact object C of T satisfying some finite tilting
assumptions, we obtain a functor which "approximates" objects of the module
category of the endomorphism algebra of C in T. This generalises and extends a
construction of Jorgensen in connection with lifts of certain homological
functors of derived categories. We show that this new functor is well-behaved
with respect to short exact sequences and distinguished triangles, and as a
consequence we obtain a new way of embedding the module category in a
triangulated category. As an example of the theory, we recover Keller’s
canonical embedding of the module category of a path algebra of a quiver with
no oriented cycles into its u-cluster category for u>1. | | Source: | arXiv, 0903.5232 | | Services: | Forum | Review | PDF | Favorites | |
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