• Title/Summary/Keyword: recollement

Search Result 3, Processing Time 0.016 seconds

THE RESOLUTION DIMENSIONS WITH RESPECT TO BALANCED PAIRS IN THE RECOLLEMENT OF ABELIAN CATEGORIES

  • Fu, Xuerong;Hu, Yonggang;Yao, Hailou
    • Journal of the Korean Mathematical Society
    • /
    • v.56 no.4
    • /
    • pp.1031-1048
    • /
    • 2019
  • In this paper we study recollements of abelian categories and balanced pairs. The main results are: recollements induce new balanced pairs from the middle category; the resolution dimensions are bounded under certain conditions. As an application, the resolution dimensions with respect to cotilting objects of abelian categories involved in recollements are recovered.

TWO DESCRIPTIONS OF RELATIVE DERIVED CATEGORIES

  • Bahiraei, Payam
    • Communications of the Korean Mathematical Society
    • /
    • v.33 no.1
    • /
    • pp.53-71
    • /
    • 2018
  • In this paper, we provide two different descriptions for a relative derived category with respect to a subcategory ${\mathcal{X}}$ of an abelian category ${\mathcal{A}}$. First, we construct an exact model structure on certain exact category which has as its homotopy category the relative derived category of ${\mathcal{A}}$. We also show that a relative derived category is equivalent to homotopy category of certain complexes. Moreover, we investigate the existence of certain recollements in such categories.

MODEL STRUCTURES AND RECOLLEMENTS INDUCED BY DUALITY PAIRS

  • Wenjing Chen;Ling Li;Yanping Rao
    • Bulletin of the Korean Mathematical Society
    • /
    • v.60 no.2
    • /
    • pp.405-423
    • /
    • 2023
  • Let (𝓛, 𝒜) be a complete duality pair. We give some equivalent characterizations of Gorenstein (𝓛, 𝒜)-projective modules and construct some model structures associated to duality pairs and Frobenius pairs. Some rings are described by Frobenius pairs. In addition, we investigate special Gorenstein (𝓛, 𝒜)-projective modules and construct some model structures and recollements associated to them.