{"paper":{"title":"Injective Objects of Monomorphism Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Keyan Song, Yuehui Zhang, Zhanping Wang","submitted_at":"2013-08-07T12:38:22Z","abstract_excerpt":"For an acyclic quiver $Q$ and a finite-dimensional algebra $A$, we give a unified form of the indecomposable injective objects in the monomorphism category ${\\rm Mon}(Q,A)$ and prove that ${\\rm Mon}(Q, A)$ has enough injective objects. As applications, we show that for a given self-injective algebra $A$, a tilting object in the stable category $\\underline{A}$-mod induces a natural tilting object in the stable monomorphism category $\\underline{\\rm Mon}(Q,A)$. We also realize the singularity category of the algebra $kQ\\otimes_k A$ as the stable monomorphism category of the module category of $A$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1551","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":""},"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"}