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Idempotent completion of triangulated categories
 J. Algebra
, 2001
"... Abstract. We show that the idempotent completion of a triangulated category has a natural structure of ..."
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Cited by 109 (11 self)
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Abstract. We show that the idempotent completion of a triangulated category has a natural structure of
Triangulated categories without models
, 2007
"... We exhibit examples of triangulated categories which are neither ..."
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Cited by 16 (6 self)
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We exhibit examples of triangulated categories which are neither
Dimensions of triangulated categories
, 2005
"... We define a dimension for a triangulated category. We prove a representability Theorem for a class of functors on finite dimensional triangulated categories. We study the dimension of the bounded derived category of an algebra or a scheme and we show in particular that the bounded derived category ..."
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Cited by 93 (1 self)
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We define a dimension for a triangulated category. We prove a representability Theorem for a class of functors on finite dimensional triangulated categories. We study the dimension of the bounded derived category of an algebra or a scheme and we show in particular that the bounded derived category
Localization theory for triangulated categories
 In Triangulated categories, volume 375 of London Math. Soc. Lecture Note Ser
, 2010
"... 2. Categories of fractions and localization functors 3 3. Calculus of fractions 9 4. Localization for triangulated categories 14 ..."
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Cited by 15 (0 self)
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2. Categories of fractions and localization functors 3 3. Calculus of fractions 9 4. Localization for triangulated categories 14
Localization for triangulated categories
"... 2. Categories of fractions and localization functors 4 3. Calculus of fractions 11 4. Localization for triangulated categories 16 ..."
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Cited by 6 (0 self)
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2. Categories of fractions and localization functors 4 3. Calculus of fractions 11 4. Localization for triangulated categories 16
On the vanishing of cohomology in triangulated categories
, 2008
"... We study the vanishing of cohomology in a triangulated category, in particular vanishing gaps and symmetry. ..."
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Cited by 2 (1 self)
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We study the vanishing of cohomology in a triangulated category, in particular vanishing gaps and symmetry.
The additivity of traces in triangulated categories
 ADV. MATH
"... We explain a fundamental additivity theorem for Euler characteristics and generalized trace maps in triangulated categories. The proof depends on a refined axiomatization of symmetric monoidal categories with a compatible triangulation. The refinement consists of several new axioms relating produc ..."
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Cited by 66 (7 self)
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We explain a fundamental additivity theorem for Euler characteristics and generalized trace maps in triangulated categories. The proof depends on a refined axiomatization of symmetric monoidal categories with a compatible triangulation. The refinement consists of several new axioms relating
INJECTIVE OBJECTS IN TRIANGULATED CATEGORIES
, 2006
"... We extend ideas and results of Benson and Krause on pureinjectives in triangulated categories. Given a generating set of compact objects in a compactly generated triangulated category T we define notions of monomorphism, exactness and injectivity relative to this set. We show that the injectives co ..."
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Cited by 2 (1 self)
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We extend ideas and results of Benson and Krause on pureinjectives in triangulated categories. Given a generating set of compact objects in a compactly generated triangulated category T we define notions of monomorphism, exactness and injectivity relative to this set. We show that the injectives
ON THE CENTER OF A TRIANGULATED CATEGORY
, 903
"... Abstract. We discuss some basic properties of the graded center of a triangulated category and compute examples arising in representation theory of finite dimensional algebras. 1. ..."
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Abstract. We discuss some basic properties of the graded center of a triangulated category and compute examples arising in representation theory of finite dimensional algebras. 1.
Results 1  10
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