A duality formalism in the spirit of Grothendieck and Verdier

By M. Boyarchenko, V. Drinfeld. 2011

56 citations recorded by the source corpus.

We study monoidal categories that enjoy a certain weakening of the rigidity property, namely, the existence of a dualizing object in the sense of Grothendieck and Verdier. We call them Grothendieck-Verdier categories. Notable examples include the derived category of constructible sheaves on a scheme (with respect to tensor product) as well as the derived and equivariant derived categories of constructible sheaves on an algebraic group (with respect to convolution). We show that the notions of pivotal category and ribbon category, which are well known in the setting of rigid monoidal categories, as well as certain standard results associated with these notions, have natural analogues in the world of Grothendieck-Verdier categories.

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

View Paper: https://www.semanticscholar.org/paper/8b52561bc0df778b6e339e0ae7f0491890f8e425

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In Geometry and Topology

1. Jürgen Fuchs
2. Christoph Schweigert
3. Gregor Schaumann
4. Liang Kong
5. Bob Coecke
6. I. Tipunin
7. A. M. Semikhatov
8. Shu-Heng Shao

In Mathematical Physics

1. Jürgen Fuchs
2. Christoph Schweigert
3. Gregor Schaumann
4. Liang Kong
5. Bob Coecke

In Statistical and Nonlinear Physics

1. Jürgen Fuchs
2. Christoph Schweigert
3. Gregor Schaumann

Citations in the corpus

• Eilenberg-Watts calculus for finite categories and a bimodule Radford 𝑆⁴ theorem (2016, methodology): “near category, the Nakayama functors and the equivalences appearing in the triangle (3.6) can be used to endow the category M=Xopp ⊠Xwith the structure of a Grothendieck-Verdier (GV) category. Recall [BoD] that a GV-structure on a monoidal category Mamounts to an object N∈Mand an equivalence DN : M→”