Monoidal Hom-Hopf algebras

TL;DR

This paper explores Hom-structures like Hom-algebras and Hom-Hopf algebras within the framework of monoidal categories, providing a categorical perspective that unifies these structures.

Contribution

It introduces a symmetric monoidal category where Hom-structures are represented as algebras, coalgebras, and Hopf algebras within this categorical setting.

Findings

Hom-structures are characterized as algebras in a new symmetric monoidal category.

Provides a unified categorical framework for Hom-algebras, coalgebras, and Hopf algebras.

Establishes properties of Hom-structures analogous to classical algebraic structures.

Abstract

Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in particular, we introduce a symmetric monoidal category such that Hom-algebras coincide with algebras in this monoidal category, and similar properties for coalgebras, Hopf algebras and Lie algebras.