{"paper":{"title":"ICE-closed subcategories and epibricks over recollements","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Jinrui Yang, Yongyun Qin","submitted_at":"2025-02-06T09:03:58Z","abstract_excerpt":"Let $( \\mathcal{A^{'}},\\mathcal{A},\\mathcal{A^{''}},i^\\ast,i_\\ast,i_!,j_!,j^\\ast,j_\\ast)$ be a recollement of abelian categories. We proved that every ICE-closed subcategory (resp. epibrick, monobrick) in $\\mathcal{A^{'}}$ or $\\mathcal{A^{''}}$ can be extended to an ICE-closed subcategories (resp. epibrick, monobrick) in $\\mathcal{A}$, and the assignment $\\mathcal{C}\\mapsto j^*(\\mathcal{C})$ defines a bijection between certain ICE-closed subcategories in $\\mathcal{A}$ and those in $\\mathcal{A}''$. Moreover, the ICE-closed subcategory $\\mathcal{C}$ of $\\mathcal{A}$ containing $i_\\ast(\\mathcal{A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.03887","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.03887/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}