Results 221 to 230 of about 82,482 (245)

Costratification and actions of tensor-triangulated categories

Documenta Mathematica, 2022
We develop the theory of costratification in the setting of relative tensor-triangular geometry, in the sense of Stevenson, providing a unified approach to classification results of Neeman and Benson–Iyengar–Krause.
Charalampos Verasdanis
semanticscholar   +1 more source

Group actions on monoidal triangulated categories and Balmer spectra

Documenta Mathematica
Let G be a group acting on a left or right rigid monoidal triangulated category \mathbf{K} which has a Noetherian Balmer spectrum. We prove that the Balmer spectrum of the crossed product category of \mathbf{K} by G is ...
Hongdi Huang, Kent B. Vashaw
semanticscholar   +1 more source

Hopf algebras are determined by their monoidal derived categories

Mathematische Zeitschrift
We show that two finite-dimensional Hopf algebras are gauge equivalent if and only if their bounded derived categories are monoidal triangulated equivalent.
Yuying Xu, Junhua Zheng
semanticscholar   +1 more source

Formalization of derived categories in Lean/mathlib

Annals of Formalized Mathematics
This paper outlines the formalization of derived categories in the mathematical library of the proof assistant Lean 4. The derived category D(C) of any abelian category C is formalized as the localization of the category of unbounded cochain complexes ...
Joël Riou
semanticscholar   +1 more source

Metric Completions of Triangulated Categories from Finite Dimensional Algebras

Applied Categorical Structures
In this paper, we study metric completions of triangulated categories in a representation-theoretic context. We provide a concrete description of completions of bounded derived categories of hereditary finite dimensional algebras of finite ...
Cyril Matoušek
semanticscholar   +1 more source

A course on derived categories

Boletim da Sociedade Paranaense de Matemática
In the forty years of existence of derived category, it was first thought as a tool in algebraic geometry, especially in the development of duality theories that were done by Hartshorne and others.
E. R. Alvares
semanticscholar   +1 more source

Derived Categories

Homological Theory of Representations, 2021
Minseon Shin
semanticscholar   +1 more source

Three notions of dimension for triangulated categories

Journal of Algebra, 2021
Alexey Elagin, Valery A Lunts
exaly  

Triangulated Categories: Derived categories and algebraic geometry

, 2010
R. Rouquier
semanticscholar   +1 more source

Triangulated Categories: Derived categories and Grothendieck duality

, 2010
A. Neeman
semanticscholar   +1 more source