Functorial Constructions for Non-associative Algebras with Applications to Quasi-bialgebras

TL;DR

This paper develops functorial methods connecting quasi-bialgebras and dual quasi-bialgebras, extending duality concepts to non-associative structures with practical examples.

Contribution

It introduces a contravariant adjunction between quasi-bialgebras and dual quasi-bialgebras, adapting the finite dual notion for non-associative cases.

Findings

Established a contravariant adjunction between categories

Extended the finite dual concept to non-associative algebras

Provided multiple illustrative examples

Abstract

The aim of this paper is to establish a contravariant adjunction between the category of quasi-bialgebras and a suitable full subcategory of dual quasi-bialgebras, adapting the notion of finite dual to this framework. Various functorial constructions involving non-associative algebras and non-coassociative coalgebras are then carried out. Several examples illustrating our methods are expounded as well.