Homotopical presentation of categories

TL;DR

This paper provides a criterion for when a functor between small categories can generate a small presentation of the universal model category, aiding in understanding categorical structures through homotopical methods.

Contribution

It introduces a new criterion for functors to produce small presentations of universal model categories, advancing categorical and homotopical theory.

Findings

Provides a criterion for functors to generate small presentations

Connects categorical functors with homotopical universal model categories

Enhances understanding of categorical structures via homotopy theory

Abstract

We give a criterion for a functor \(F:C\rightarrow B\) between small categories to generate a small presentation of the universal model category \(U(B)\) in the sense of Dugger.