Braided bialgebras in a generated monoidal Ab-category

TL;DR

This paper develops a method to extend any small strict monoidal braided Ab-category into a nonstrict braided Ab-category containing braided bialgebras, with original objects acting as modules for these bialgebras.

Contribution

It introduces a construction that embeds objects of a given category as modules over newly formed braided bialgebras within an extended category.

Findings

Objects of the original category become modules for the constructed braided bialgebras.

Extension from strict to nonstrict braided Ab-category is achieved.

The approach generalizes the structure of braided bialgebras in monoidal categories.

Abstract

We start from any small strict monoidal braided Ab-category and extend it to a monoidal nonstrict braided Ab-category which contains braided bialgebras. The objects of the original category turn out to be modules for these bialgebras