# Quandle Cocycle Quivers

## TL;DR

This paper introduces quandle cocycle quivers, a new categorification of quandle cocycle invariants for links, using weighted directed graphs to produce novel link invariants including a 2-variable polynomial.

## Contribution

It develops quandle cocycle quivers, integrating cocycle data into quandle coloring quivers to create categorified link invariants and new polynomial invariants.

## Key findings

- Defines quandle cocycle quivers as weighted directed graphs for links
- Provides examples and computations demonstrating the invariants
- Introduces a 2-variable polynomial invariant that generalizes the quandle cocycle invariant

## Abstract

We incorporate quandle cocycle information into the quandle coloring quivers we defined in arXiv:1807.10465 to define weighted directed graph-valued invariants of oriented links we call \textit{quandle cocycle quivers}. This construction turns the quandle cocycle invariant into a small category, yielding a categorification of the quandle cocycleinvariant. From these graphs we define several new link invariants including a 2-variable polynomial which specializes to the usual quandle cocycle invariant. Examples and computations are provided.