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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 196 (4 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.
Homotopical algebraic geometry. II. Geometric stacks and applications
, 2006
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A closed model structure for ncategories, internal Hom, nstacks and generalized SeifertVan Kampen
, 1997
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Homotopy Theory of Higher Categories
"... portant la référence ANR09BLAN015102 (HODAG). This is draft material from a forthcoming book to be published by Cambridge University Press in the New Mathematical Monographs series. This publication is in copyright. c○Carlos T. Simpson 2010. v This is the first draft of a book about higher categ ..."
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Cited by 23 (0 self)
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portant la référence ANR09BLAN015102 (HODAG). This is draft material from a forthcoming book to be published by Cambridge University Press in the New Mathematical Monographs series. This publication is in copyright. c○Carlos T. Simpson 2010. v This is the first draft of a book about higher categories approached by iterating Segal’s method, as in Tamsamani’s definition of nnerve and Pelissier’s thesis. If M is a tractable left proper cartesian model
Motivic structures in noncommutative geometry. Available at arXiv:1003.3210
 the Proceedings of the ICM
, 2010
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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 16 (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 5 (1 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