The derived and extension dimensions of abelian categories

DOI10.1016/j.jalgebra.2022.05.003zbMath1489.18005arXiv2205.04133OpenAlexW4280489688MaRDI QIDQ2144377

Junling Zheng, Zhao Yong Huang

Publication date: 13 June 2022

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.04133

zbMATH Keywords

extension dimensionfinite typeabelian categoriesrelative projective dimensionderived dimensionradical layer lengthrelative injective dimension(Co)resolving subcategories

Mathematics Subject Classification ID

Homological dimension (category-theoretic aspects) (18G20) Abelian categories, Grothendieck categories (18E10) Homological dimension in associative algebras (16E10) Derived categories, triangulated categories (18G80)

Related Items (2)

Extension dimensions of derived and stable equivalent algebras ⋮ The derived dimensions of \((m,n)\)-Igusa-Todorov algebras

Cites Work

• Homological theory of recollements of abelian categories
• Representation dimension of Artin algebras.
• Frobenius algebras. I: Basic representation theory.
• Lower bounds for Auslander's representation dimension.
• Finitistic dimension and Igusa-Todorov algebras.
• Orlov spectra: bounds and gaps
• Applications of contravariantly finite subcategories
• An upper bound for the dimension of bounded derived categories
• The extension dimension of abelian categories
• Layer lengths, torsion theories and the finitistic dimension
• Representation dimension of exterior algebras
• The radius of a subcategory of modules
• Generating the bounded derived category and perfect ghosts
• Remarks on generators and dimensions of triangulated categories
• THE GORENSTEIN DEFECT CATEGORY
• Algebras of Derived Dimension Zero
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