DEFINABILITY AND APPROXIMATIONS IN TRIANGULATED CATEGORIES

被引：15
作者：
Laking, Rosanna [1 ]
Vitoria, Jorge [2 ]
机构：
[1] Univ Verona, Dipartimento Informat, Verona, Italy
[2] Univ Cagliari, Dipartimento Matemat & Informat, Cagliari, Italy
来源：
PACIFIC JOURNAL OF MATHEMATICS | 2020年 / 306卷 / 02期
基金：
英国工程与自然科学研究理事会;
关键词：
precover; preenvelope; definable subcategory; torsion pair; t-structure; recollement; CO-T-STRUCTURES; TORSION PAIRS; ADJOINTS; COVERS; RINGS; FUNCTORS; OBJECTS;
D O I：
10.2140/pjm.2020.306.557
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：557 / 586
页数：30
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