A new approach to model categorical homotopy fiber sequences

TL;DR

This paper introduces a simplified, action-independent definition of Quillen's fibration sequences within pointed model categories, emphasizing the homotopy theory of the arrow category as a comprehensive framework.

Contribution

It provides a new, streamlined approach to modeling homotopy fiber sequences that captures the full theory without relying on actions.

Findings

Simplified definition of Quillen's fibration sequences

Full capture of the theory independent of actions

Homotopy theory of arrow category contains all relevant information

Abstract

We propose a simplified definition of Quillen's fibration sequences in a pointed model category that fully captures the theory, although it is completely independent of the concept of action. This advantage arises from the understanding that the homotopy theory of the model category's arrow category contains all homotopical information about its long fibration sequences.