What do dg-categories form?

Dmitry Tamarkin

doi:10.1112/S0010437X07002771

Abstract

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We introduce a homotopy 2-category structure on the collection of dg-categories, dg-functors, and their derived transformations. This construction provides for a conceptual proof of Deligne's conjecture on Hochschild cochains.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Dolgushev, Vasiliy Tamarkin, Dmitry and Tsygan, Boris 2009. Formality Theorems for Hochschild Complexes and Their Applications. Letters in Mathematical Physics, Vol. 90, Issue. 1-3, p. 103.

Tabuada, Gonçalo 2010. On Drinfeld's DG quotient. Journal of Algebra, Vol. 323, Issue. 5, p. 1226.

Dolgushev, V. A. Tamarkin, D. E. and Tsygan, B. L. 2010. Proof of Swiss Cheese Version of Deligne's Conjecture. International Mathematics Research Notices,

Batanin, Michael and Markl, Martin 2012. Centers and homotopy centers in enriched monoidal categories. Advances in Mathematics, Vol. 230, Issue. 4-6, p. 1811.

Loday, Jean-Louis and Vallette, Bruno 2012. Algebraic Operads. Vol. 346, Issue. , p. 479.

Dolgushev, Vasily A. Hoffnung, Alexander E. and Rogers, Christopher L. 2015. What do homotopy algebras form?. Advances in Mathematics, Vol. 274, Issue. , p. 562.

Batanin, Michael and Markl, Martin 2015. Operadic categories and duoidal Deligne's conjecture. Advances in Mathematics, Vol. 285, Issue. , p. 1630.

Dolgushev, Vasily and Willwacher, Thomas 2015. Operadic twisting – With an application to Deligne's conjecture. Journal of Pure and Applied Algebra, Vol. 219, Issue. 5, p. 1349.

Bourke, John and Garner, Richard 2016. Algebraic weak factorisation systems II: Categories of weak maps. Journal of Pure and Applied Algebra, Vol. 220, Issue. 1, p. 148.

Berest, Yuri Eshmatov, Alimjon and Yeung, Wai-Kit 2017. Perverse sheaves and knot contact homology. Comptes Rendus. Mathématique, Vol. 355, Issue. 4, p. 378.

Dolgushev, Vasily and Willwacher, Thomas 2017. A direct computation of the cohomology of the braces operad. Forum Mathematicum, Vol. 29, Issue. 2, p. 465.

Paoli, Simona 2019. Simplicial Methods for Higher Categories. Vol. 26, Issue. , p. 3.

Paoli, Simona 2019. Simplicial Methods for Higher Categories. Vol. 26, Issue. , p. 315.

Kaledin, Dmitry Borisovich 2022. Что образуют абелевы категории?. Успехи математических наук, Vol. 77, Issue. 1(463), p. 3.

Shoikhet, Boris 2023. The twisted tensor product of dg categories and a contractible 2-operad. Advances in Mathematics, Vol. 434, Issue. , p. 109310.

Benini, Marco Musante, Giorgio and Schenkel, Alexander 2023. Green Hyperbolic Complexes on Lorentzian Manifolds. Communications in Mathematical Physics, Vol. 403, Issue. 2, p. 699.

Article contents

What do dg-categories form?

Abstract

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

What do dg-categories form?

Abstract

Keywords

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