On equivariant triangulated categories

2014/03/27 by Alexey Elagin, Elagin, Alexey · 5 citations
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1403.7027

openalex publication_date 2014/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider a finite group G acting on a triangulated category \mathcal T. In this paper we investigate triangulated structure on the category \mathcal T^G of G-equivariant objects in \mathcal T. We prove (under some technical conditions) that such structure exists. Supposed that an action on \mathcal T is induced by a DG-action on some DG-enhancement of \mathcal T, we construct a DG-enhancement of \mathcal T^G. 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.

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• Noncommutative Knörrer periodicity via equivariantization
• Rational points on symmetric powers and categorical representability

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