Stability for inner fibrations revisited

TL;DR

This paper revisits the stability of inner fibrations in simplicial sets, establishing new results using the wide join operation and exploring properties of inner anodyne morphisms.

Contribution

It introduces a stability theorem for inner fibrations via the wide join and provides new insights into inner anodyne morphisms.

Findings

Proves a stability result for inner fibrations using the wide join operation.

Establishes additional properties of inner anodyne morphisms.

Enhances understanding of the structure of simplicial sets.

Abstract

In this paper we prove a stability result for inner fibrations in terms of the wide, or fat join operation on simplicial sets. We also prove some additional results on inner anodyne morphisms that may be of independent interest.