# From biquandle structures to Hom-biquandles

## TL;DR

This paper explores the connection between biquandle and quandle invariants, introduces enhancements using biquandle structures, and studies the properties of Hom-biquandles and their relationship to Hom-quandles.

## Contribution

It provides new insights into biquandle structures, develops biquandle analogs of Hom-quandle results, and describes the structure of Hom-biquandles.

## Key findings

- Enhanced quandle and biquandle invariants using biquandle structures
- Biquandle analogs of Hom-quandle results
- Description of the biquandle structure of Hom-biquandles

## Abstract

We investigate the relationship between the quandle and biquandle coloring invariant and obtain an enhancement of the quandle and biquandle coloring invariants using biquandle structures. We also continue the study of biquandle homomorphisms into a medial biquandle begun by the second author et al., finding biquandle analogs of results about Hom-quandles. We describe the biquandle structure of the Hom-biquandle, and consider the relationship between the Hom-quandle and Hom-biquandle.