On differential graded categories

By B. Keller. 2006

730 citations recorded by the source corpus.

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, Dugger�Shipley, Toen, Toen�Vaquie, and others.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bfb70e2c2e7545afa5f78e8967d4f61f172c586a

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Derived algebraic geometry (2014, background): “The morphism is assumed to be a morphism of mixed complexes, for the natural mixed structure on HH (T ) (see [76]), and the trivial mixed structure on k[−d].”
Parametrizing recollement data for triangulated categories (2009, background): “[27] for the notation) formed by the H-injective or fibrant resolutions iP [23,27] of the modules P of P .”
Derived Categories View on Rationality Problems (2015, background): “There is a powerful machinery (see [GM99] for the classical or [Kel06] for the modern approach) which allows to extend an additive functor between abelian categories to a triangulated functor between their derived categories.”
On exact categories and applications to triangulated adjoints and model structures (2010, background): “Such triangulated categories are called algebraic, see [34, 39].”
Loop spaces and connections (2010, background): “(Among the many excellent references for dg and A∞-categories, we recommend [10] and the survey [19].”
Categorical resolutions of irrational singularities (2012, background): “A general reference for DG-categories is an excellent review of Keller [Ke06].”
Koszul equivalences in A ∞ -algebras (2008, background): “A good reference for the derived category D(R) is [19]; also see [21, 22].”
Chern characters and Hirzebruch-Riemann-Roch formula for matrix factorizations (2010, background): “The perfect derived category Per(C) ⊂ D(C) is the full subcategory of compact objects in D(C) (see [16]).”
A Guided Tour Through the Garden of Noncommutative Motives (2011, background): “Note first that all the classical constructions which can be performed with kalgebras can also be performed with dg categories; consult [28].”