Strong Hopf modules for weak Hopf quasigroups

TL;DR

This paper introduces the category of strong Hopf modules for weak Hopf quasigroups within a braided monoidal category and proves its equivalence to a module category over a specific morphism image.

Contribution

It defines strong Hopf modules for weak Hopf quasigroups and establishes an equivalence with a module category, advancing the algebraic understanding of these structures.

Findings

Category of strong Hopf modules is equivalent to right modules over the target morphism image.

Provides a new framework for studying weak Hopf quasigroups in braided monoidal categories.

Establishes foundational results for future algebraic and categorical research.

Abstract

In this paper we introduce the category of strong Hopf modules for a weak Hopf quasigroup H in a braided monoidal category. We also prove that this category is equivalent to the category of right modules over the image of the target morphism of H.