{"paper":{"title":"(Co)cyclic (co)homology of bialgebroids: An approach via (co)monads","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"math.KT","authors_text":"Dragos Stefan, Gabriella B\\\"ohm","submitted_at":"2007-05-22T15:34:01Z","abstract_excerpt":"For a (co)monad T_l on a category M, an object X in M, and a functor \\Pi: M \\to C, there is a (co)simplex Z^*:=\\Pi T_l^{* +1} X in C. Our aim is to find criteria for para-(co)cyclicity of Z^*. Construction is built on a distributive law of T_l with a second (co)monad T_r on M, a natural transformation i:\\Pi T_l \\to \\Pi T_r, and a morphism w: T_r X \\to T_l X in M. The relations i and w need to satisfy are categorical versions of Kaygun's axioms of a transposition map. Motivation comes from the observation that a (co)ring T over an algebra R determines a distributive law of two (co)monads T_l=T "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.3190","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"}