Definability and approximations in triangulated categories

Vitória, Jorge
2020-01-01

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 sub-category 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.
2020
2020
Inglese
PACIFIC JOURNAL OF MATHEMATICS
306
2
557
586
30
WOS:000575404000007
2-s2.0-85091118961
Esperti anonimi
scientifica
precover; preenvelope; definable subcategory; torsion pair; t-structure; recollement
no
Laking, Rosanna; Vitória, Jorge
1.1 Articolo in rivista
info:eu-repo/semantics/article
1 Contributo su Rivista::1.1 Articolo in rivista
262
2
reserved
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