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Definability and approximations in triangulated categories

By Rosanna Laking and Jorge Vitória

Abstract

We give criteria for subcategories of a compactly generated algebraic triangulated category to be precovering or preenveloping. These criteria are formulated in terms of closure conditions involving products, coproducts, directed homotopy colimits and further conditions involving the notion of purity. In particular, we provide sufficient closure conditions for a subcategory of a compactly generated algebraic triangulated category to be a torsion class. Finally we explore applications of the previous results to the theory of recollements.Comment: Updated version with new Proposition 6.1

Topics: Mathematics - Representation Theory, Mathematics - Category Theory, Mathematics - Rings and Algebras, 18C35, 18E30, 18E35, 18E40
Publisher: 'Mathematical Sciences Publishers'
Year: 2018
DOI identifier: 10.2140/pjm.2020.306.557
OAI identifier: oai:arXiv.org:1811.00340

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