# Exceptional collections in surface-like categories

## TL;DR

This paper develops a categorical framework to analyze and generalize results on exceptional collections in surface-like categories, simplifying existing criteria and expanding their applicability.

## Contribution

It introduces a new categorical approach that simplifies and broadens the understanding of exceptional collections on numerically rational surfaces.

## Key findings

- Unified categorical framework for exceptional collections
- Simplified criteria for existence of numerical exceptional collections
- Generalizations of previous results by Perling and Vial

## Abstract

We provide a categorical framework for recent results of Markus Perling on combinatorics of exceptional collections on numerically rational surfaces. Using it we simplify and generalize some of Perling's results as well as Vial's criterion for existence of a numerical exceptional collection.