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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1301.2853","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-01-14T03:22:10Z","cross_cats_sorted":[],"title_canon_sha256":"f8f9c3cab3b69d01bd0a65c2d1a340be111fea8b97f90d8f64a633d56c0c6b01","abstract_canon_sha256":"46145e84ada3e8f82e2c1e31371edbc796c6fffdce6a7bc446a9413ba26e27b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:34.984437Z","signature_b64":"0lNu3qLuK8KxA11tSIKHP9kShcq99pUccbZfBA0kWUYTTXE20wJuiuTU1/0yMtOJaoVzZae3sfgEvcZmQzxyAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a450aaed2b30d1a5dd3e8eefb065a42637045acac87681c2d9fa09aae2c76d2","last_reissued_at":"2026-05-18T03:36:34.983617Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:34.983617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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