{"paper":{"title":"Operadic comodules and (co)homology theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"James Griffin","submitted_at":"2014-03-19T14:58:23Z","abstract_excerpt":"An operad describes a category of algebras and a (co)homology theory for these algebras may be formulated using the homological algebra of operads. A morphism of operads $f:\\mathcal{O}\\rightarrow\\mathcal{P}$ describes a functor allowing a $\\mathcal{P}$-algebra to be viewed as an $\\mathcal{O}$-algebra. We show that the $\\mathcal{O}$-algebra (co)homology of a $\\mathcal{P}$-algebra may be represented by a certain operadic comodule. Thus filtrations of this comodule result in spectral sequences computing the (co)homology.\n  As a demonstration we study operads with a filtered distributive law; for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4831","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"}