On the abelianization of derived categories and a negative solution to Rosicky's problem
Category Theory
2019-02-20 v1 Algebraic Topology
K-Theory and Homology
Rings and Algebras
Abstract
We prove for a large family of rings R that their lambda-pure global dimension is greater than one for each infinite regular cardinal lambda. This answers in negative a problem posed by Rosicky. The derived categories of such rings then do not satisfy the Adams lambda-representability for morphisms for any lambda. Equivalently, they are examples of well generated triangulated categories whose lambda-abelianization in the sense of Neeman is not a full functor for any lambda. In particular we show that given a compactly generated triangulated category, one may not be able to find a Rosicky functor among the lambda-abelianization functors.
Keywords
Cite
@article{arxiv.1102.3240,
title = {On the abelianization of derived categories and a negative solution to Rosicky's problem},
author = {Silvana Bazzoni and Jan Stovicek},
journal= {arXiv preprint arXiv:1102.3240},
year = {2019}
}
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24 pages