Characterizing model structures on finite posets

TL;DR

This paper provides a complete characterization of all model category structures on finite lattices by leveraging transfer systems, bridging abstract homotopy theory and equivariant methods.

Contribution

It introduces a comprehensive classification of model structures on finite lattices using transfer systems, revealing new links between homotopy theory and equivariant techniques.

Findings

Complete characterization of model structures on finite lattices

Identification of transfer systems as key tools in classification

New connections established between homotopy theory and equivariant methods

Abstract

Transfer systems on finite posets have recently been gaining traction as a key ingredient in equivariant homotopy theory. Additionally, they also naturally occur in the data of a model structure. We give a complete characterization of all model category structures on a finite lattice, using transfer systems as our main tool, resulting in new connections between abstract homotopy theory and equivariant methods.