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.

DEFINABILITY AND APPROXIMATIONS IN TRIANGULATED CATEGORIES

Laking, R.
;
Vitória, J.
2020

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.
precover
preenvelope
definable subcategory
torsion pair
t-structure
recollement
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11562/1056439
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