{"paper":{"title":"Monomorphism operator and perpendicular operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Keyan Song, Pu Zhang","submitted_at":"2013-01-14T03:22:10Z","abstract_excerpt":"For a quiver $Q$, a $k$-algebra $A$, and a full subcategory $\\mathcal X$ of $A$-mod, the monomorphism category ${\\rm Mon}(Q, \\mathcal X)$ is introduced. The main result says that if $T$ is an $A$-module such that there is an exact sequence $0\\rightarrow T_m\\rightarrow...\\rightarrow T_0\\rightarrow D(A_A)\\rightarrow 0$ with each $T_i\\in {\\rm add} (T)$, then ${\\rm Mon}(Q, \\ ^\\perp T) = \\ ^\\perp (kQ\\otimes_k T)$; and if $T$ is cotilting, then $kQ\\otimes_k T$ is a unique cotilting $\\m$-module, up to multiplicities of indecomposable direct summands, such that ${\\rm Mon}(Q, \\ ^\\perp T)= \\ ^\\perp (kQ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2853","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"}