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Tensor Triangulated Categories of Algebraic Structures: Bridging Groups, Rings, and Derived Fields

This paper explores the unifying framework of tensor triangulated categories (TTCs) to study diverse algebraic structures. We establish how the abstract machinery of TTCs, combining the axioms of a triangulated category with a compatible symmetric monoidal structure, provides a common language to analyze groups, rings, and the modern notion of derived ...
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Three notions of dimension for triangulated categories

Journal of Algebra, 2021
Alexey Elagin, Valery Lunts
exaly  

Idempotent Completion of Triangulated Categories

Journal of Algebra, 2001
Paul Balmer
exaly  

Parametrizing recollement data for triangulated categories

Journal of Algebra, 2009
Pedro Nicolas, Manuel SaorĂ­n
exaly  

Dimensions of triangulated categories via Koszul objects

Mathematische Zeitschrift, 2009
Srikanth B Iyengar, Henning Krause
exaly  

Triangulated Quotient Categories

Communications in Algebra, 2013
Bin Zhu
exaly  

Triangulated quotient categories revisited

Journal of Algebra, 2018
Panyue Zhou, Bin Zhu
exaly  

Cotorsion Pairs in a Recollement of Triangulated Categories

Communications in Algebra, 2013
Jianmin Chen
exaly  

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