The universal Hopf-cyclic theory

Atabey Kaygun*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


We define a Hopf cyclic (co)homology theory in an arbitrary symmetric strict monoidal category. Thus we unify all different types of Hopf cyclic (co)homologies under one single universal theory. We recover Hopf cyclic (co)homology of module algebras, comodule algebras and module coalgebras along with Hopf-Hochschild (co)homology of module algebras, and describe the missing theory for comodule coalgebras.

Original languageEnglish
Pages (from-to)333-351
Number of pages19
JournalJournal of Noncommutative Geometry
Issue number3
Publication statusPublished - 2008
Externally publishedYes


  • Hopf-cyclic cohomology
  • Monads
  • Transpositive algebras


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