2025/01/24 by Ivan Bartulović, Bartulović, Ivan, John Boiquaye +3
Mathematics · #18C15 #19D55 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.2501.14561
openalex publication_date 2025/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Böhm and Ştefan have expressed cyclic homology as an invariant that assigns homology groups HCχi(\mathrm N, \mathrm M) to right and left coalgebras \mathrm N respectively \mathrm M over a distributive law χ between two comonads. For the key example associated to a bialgebra H, right χ-coalgebras have a description in terms of modules and comodules over H. The present article formulates conditions under which such a description is simultaneously possible for the left χ-coalgebras. In the above example, this is the case when the bialgebra H is a Hopf algebra with bijective antipode. We also discuss how the generalized Hopf module theorem by Mesablishvili and Wisbauer features both in theory and examples.