Smash coproducts of bicomonads and Hom-entwining structures

TL;DR

This paper explores the construction of smash coproducts of bicomonads in monoidal categories, with applications to Hom-bialgebras and the study of Hom-entwining structures and modules.

Contribution

It introduces the concept of smash coproducts for bicomonads and applies it to Hom-bialgebras, advancing the understanding of Hom-entwining structures.

Findings

Defined smash coproducts of bicomonads.

Applied smash coproducts to Hom-bialgebras.

Investigated Hom-entwining structures and modules.

Abstract

Let $F,G$ be bicomonads on a monoidal category $\mathcal{C}$. The aim of this paper is to discuss the smash coproducts of $F$ and $G$. As an application, the smash coproduct of Hom-bialgebras is discussed. Further, the Hom-entwining structure and Hom-entwined modules are investigated.