# Simple transitive $2$-representations of some $2$-categories of projective functors

## TL;DR

This paper proves that all simple transitive 2-representations of a specific 2-category of projective functors are equivalent to cell 2-representations, clarifying their structure in a particular algebraic setting.

## Contribution

It establishes the equivalence of simple transitive 2-representations to cell 2-representations for a class of 2-categories related to projective functors.

## Key findings

- All simple transitive 2-representations are equivalent to cell 2-representations.
- The result applies to a 2-category associated with a quotient of the quadratic dual of a preprojective algebra.
- Provides a classification of simple transitive 2-representations in this context.

## Abstract

We show that every simple transitive $2$-representation of the $2$-category of projective functors for a certain quotient of the quadratic dual of the preprojective algebra associated with a tree is equivalent to a cell $2$-representation.