Une structure de catégorie de modèles de Quillen sur la catégorie des dg-catégories

By Goncalo Tabuada. 2004

161 citations recorded by the source corpus.

Resume Nous construisons une structure de categorie de modeles de Quillen a engendrement cofibrant sur la categorie des petites categories differentielles graduees. Pour citer cet article : G. Tabuada, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/37cc8e59c0bf0dd3ea4db2c3b512ee04acb8ed31

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In Geometry and Topology

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Differential Graded Categories are k-linear Stable Infinity Categories (2013, background): “utations in this setting. Stable ∞-categories are an alternative enhancement of triangulated categories that are more general than dg categories and are amenable to universal properties. In [To1] and [Tab2], To¨en and Tabuada construct a model category structure on the category of diﬀerential graded”
Higher Segal Spaces (2012, methodology): “Recall [Tab05] that dgcatF carries a combinatorial model structure in which weak equivalences are quasi-equivalences and fibrations are objectwise surjective dg transformations of dg functors.”
A Survey of (∞, 1)-Categories (2010, methodology): “Similar work is also being done using dg categories, which are in many ways analogous to simplicial categories [35].”
Hirzebruch–Riemann–Roch‐type formula for DG algebras (2007, background): “The real definition is more subtle and we won’t discuss it here referring the reader to more thorough treatments of the subject [20, 35, 62, 63, 65, 66].”
Dwyer–Kan homotopy theory of enriched categories (2012, background): “Their hypotheses are more general than Lurie’s, in particular they cover Tabuada’s and Amrani’s results.”
Hochschild (co)homology of the second kind I (2010, background): “The cofibrant DG-categories are exactly (up to the zero object issue) the cofibrant objects in the model category structure constructed in [20] (see also [21]).”
Spherical DG-functors (2013, methodology): “es of two complexes and morphisms between their classes in the derived category. One way to understand the morphism set [A;B] in Ho(DG-Cat) is via the model category structure on DG-Catconstructed in [Tab05]. The weak equivalences are the quasi-equivalences, and the brations are dened in such a way ”