{"paper":{"title":"Monoidal ring and coring structures obtained from wreaths and cowreaths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"D. Bulacu, S. Caenepeel","submitted_at":"2013-02-22T15:53:51Z","abstract_excerpt":"Let $A$ be an algebra in a monoidal category $\\Cc$, and let $X$ be an object in $\\Cc$. We study $A$-(co)ring structures on the left $A$-module $A\\ot X$. These correspond to (co)algebra structures in $EM(\\Cc)(A)$, the Eilenberg-Moore category associated to $\\Cc$ and $A$. The ring structures are in bijective correspondence to wreaths in $\\Cc$, and their category of representations is the category of representations over the induced wreath product. The coring structures are in bijective correspondence to cowreaths in $\\Cc$, and their category of corepresentations is the category of generalized en"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5626","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"}