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On differential graded categories
 INTERNATIONAL CONGRESS OF MATHEMATICIANS. VOL. II
, 2006
"... Differential graded categories enhance our understanding of triangulated categories appearing in algebra and geometry. In this survey, we review their foundations and report on recent work by Drinfeld, DuggerShipley,..., Toën and ToënVaquié. ..."
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Cited by 66 (3 self)
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Differential graded categories enhance our understanding of triangulated categories appearing in algebra and geometry. In this survey, we review their foundations and report on recent work by Drinfeld, DuggerShipley,..., Toën and ToënVaquié.
A closed model structure for ncategories, internal Hom, nstacks and generalized SeifertVan Kampen
, 1997
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Homotopical algebraic geometry. II. Geometric stacks and applications
, 2006
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Derived Hall algebras
"... The purpose of this work is to define a derived Hall algebra DH(T), associated to any dgcategory T (under some finiteness conditions). Our main theorem states that DH(T) is associative and unital. This provides an alternative to the nonexistence of Hall algebras for triangulated categories. Conten ..."
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Cited by 12 (1 self)
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The purpose of this work is to define a derived Hall algebra DH(T), associated to any dgcategory T (under some finiteness conditions). Our main theorem states that DH(T) is associative and unital. This provides an alternative to the nonexistence of Hall algebras for triangulated categories. Contents
Limits in ncategories
, 1997
"... One of the main notions in category theory is the notion of limit. Similarly, one of the most commonly used techniques in homotopy theory is the notion of “homotopy limit” commonly called “holim ” for short. The purpose of the this paper is to begin to develop ..."
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Cited by 4 (0 self)
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One of the main notions in category theory is the notion of limit. Similarly, one of the most commonly used techniques in homotopy theory is the notion of “homotopy limit” commonly called “holim ” for short. The purpose of the this paper is to begin to develop
DOI: 10.1215/S0012709406135366 Derived Hall algebras
, 2006
"... The purpose of this work is to define a derived Hall algebra DH(T), associated to any dgcategory T (under some finiteness conditions), generalizing the Hall algebra of an abelian category. Our main theorem states that DH(T) is associative and unital. When the associated triangulated category [T] is ..."
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The purpose of this work is to define a derived Hall algebra DH(T), associated to any dgcategory T (under some finiteness conditions), generalizing the Hall algebra of an abelian category. Our main theorem states that DH(T) is associative and unital. When the associated triangulated category [T] is endowed with a tstructure with heart A, it is shown that DH(T) contains the usual Hall algebra H(A). We will also prove an explicit formula for the derived Hall numbers purely in terms of invariants of the triangulated category associated to T. As an example, we describe the derived Hall algebra of an hereditary abelian category. 2000 MSC: 18G55 Contents