{"paper":{"title":"Categories of comodules and chain complexes of modules","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"A. Ardizzoni, C. Menini, L. El Kaoutit","submitted_at":"2010-04-26T16:51:37Z","abstract_excerpt":"Let $\\lL(A)$ denote the coendomorphism left $R$-bialgebroid associated to a left finitely generated and projective extension of rings $R \\to A$ with identities. We show that the category of left comodules over an epimorphic image of $\\lL(A)$ is equivalent to the category of chain complexes of left $R$-modules. This equivalence is monoidal whenever $R$ is commutative and $A$ is an $R$-algebra. This is a generalization, using entirely new tools, of results by B. Pareigis and D. Tambara for chain complexes of vector spaces over fields. Our approach relies heavily on the non commutative theory of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.4572","kind":"arxiv","version":2},"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"}