English

ICE-closed subcategories and epibricks over recollements

Representation Theory 2025-02-07 v1 Category Theory

Abstract

Let (A,A,A,i,i,i!,j!,j,j)( \mathcal{A^{'}},\mathcal{A},\mathcal{A^{''}},i^\ast,i_\ast,i_!,j_!,j^\ast,j_\ast) be a recollement of abelian categories. We proved that every ICE-closed subcategory (resp. epibrick, monobrick) in A\mathcal{A^{'}} or A\mathcal{A^{''}} can be extended to an ICE-closed subcategories (resp. epibrick, monobrick) in A\mathcal{A}, and the assignment Cj(C)\mathcal{C}\mapsto j^*(\mathcal{C}) defines a bijection between certain ICE-closed subcategories in A\mathcal{A} and those in A\mathcal{A}''. Moreover, the ICE-closed subcategory C\mathcal{C} of A\mathcal{A} containing i(A)i_\ast(\mathcal{A^{'}}) admits a new recollement relative to ICE-closed subcategories A\mathcal{A^{'}} and j(C)j^\ast(\mathcal{C}) which induced from the original recollement when j!j(C)Cj_!{j^\ast(\mathcal{C})}\subset\mathcal{C}.

Cite

@article{arxiv.2502.03887,
  title  = {ICE-closed subcategories and epibricks over recollements},
  author = {Jinrui Yang and Yongyun Qin},
  journal= {arXiv preprint arXiv:2502.03887},
  year   = {2025}
}
R2 v1 2026-06-28T21:34:31.432Z