Uniqueness of pairings in Hopf-cyclic cohomology

TL;DR

This paper demonstrates that all existing pairings extending the Connes-Moscovici characteristic map in Hopf-cyclic cohomology are essentially equivalent as natural transformations, unifying various approaches.

Contribution

It proves the isomorphism of all such pairings, establishing their fundamental equivalence in the context of Hopf-cyclic cohomology.

Findings

All pairings are isomorphic as natural transformations.

Unifies different pairings in Hopf-cyclic cohomology.

Provides a canonical perspective on the characteristic map.

Abstract

We show that all pairings defined in the literature extending Connes-Moscovici characteristic map in Hopf-cyclic cohomology are isomorphic as natural transformations of derived double functors.