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Definability and
approximations in triangulated categories
Rosanna Laking and Jorge Vitória |
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Vol. 306 (2020), No. 2, 557–586
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Abstract |
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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. |
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Keywords
precover, preenvelope, definable subcategory, torsion pair,
t-structure, recollement
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Mathematical Subject Classification 2010
Primary: 18C35, 18E30, 18E35, 18E40
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Milestones
Received: 30 April 2019
Revised: 16 December 2019
Accepted: 9 January 2020
Published: 13 July 2020
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Authors |
| Rosanna Laking | |
| Dipartimento di Informatica Università degli Studi di Verona Verona Italy |
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| Jorge Vitória | |
| Dipartimento di Matematica e
Informatica Università degli Studi di Cagliari Cagliari Italy |
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