{"paper":{"title":"Monomorphisms of Coalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"A.L. Agore","submitted_at":"2009-08-20T16:49:40Z","abstract_excerpt":"We prove new necessary and sufficient conditions for a morphism of coalgebras to be a monomorphism, different from the ones already available in the literature. More precisely, $\\phi: C \\to D$ is a monomorphism of coalgebras if and only if the first cohomology groups of the coalgebras $C$ and $D$ coincide if and only if $\\sum_{i \\in I}\\epsilon(a^{i})b^{i} = \\sum_{i \\in I} a^{i} \\epsilon(b^{i})$, for all $\\sum_{i \\in I}a^{i} \\otimes b^{i} \\in C \\square_{D} C$. In particular, necessary and sufficient conditions for a Hopf algebra map to be a monomorphism are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.2959","kind":"arxiv","version":3},"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"}