ON EQUIVARIANT TRIANGULATED CATEGORIES

By A. Elagin. 2014

70 citations recorded by the source corpus.

Consider a finite group G acting on a triangulated category T. In this paper we try to understand when the category T G of G-equivariant objects in T is triangulated. We prove that it is so in two cases: the action on the derived category D b (A) induced by an action on an abelian category A and the action on the homotopy category H 0 (A) of a pretriangulated DG-category A induced by an action on A. Also, we show that the relation "to be an equivariant category with respect to a finite abelian group action" is symmetric on idempotent complete additive categories.

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

View Paper: https://www.semanticscholar.org/paper/a2320f23b91ab143edd8f732bde50efefd3764ac

How researchers see this paper

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In Algebra and Number Theory

1. Arend Bayer
2. P. Stellari
3. Emanuele Macrì
4. Michael Usher
5. P. Seidel
6. C. Teleman
7. V. Golyshev

In Geometry and Topology

1. Emanuele Macrì
2. Arend Bayer
3. P. Stellari
4. Chunyi Li
5. D. Huybrechts
6. Benjamin Schmidt
7. Yukinobu Toda
8. Xiaolei Zhao

In Mathematical Physics

1. Emanuele Macrì
2. Arend Bayer
3. P. Stellari
4. D. Huybrechts
5. Chunyi Li
6. Yukinobu Toda
7. Benjamin Schmidt
8. Alexander Kuznetsov

Citations in the corpus

• The space of stability conditions on abelian threefolds, and on some Calabi-Yau threefolds (2014, background): “As explained in [17], the category Db([X/G]) is equivalent to the category of theG-equivariant objects inDb(X).”