Linear versus set valued Kronecker representations

TL;DR

This paper compares linear and set valued representations of the Kronecker quiver by applying a forgetful functor from vector spaces to sets, highlighting differences and similarities.

Contribution

It introduces a novel comparison between linear and set valued representations of the Kronecker quiver using categorical functors.

Findings

Set valued representations form a quiver structure.

Differences between linear and set representations are characterized.

Insights into the categorical relationship between representations.

Abstract

A set valued representation of the Kronecker quiver is nothing but a quiver. We apply the forgetful functor from vector spaces to sets and compare linear with set valued representations of the Kronecker quiver.