A Quillen model structure for bigroupoids and pseudofunctors

TL;DR

This paper constructs a model structure for small bigroupoids and pseudofunctors, establishing cofibrancy of all objects and providing coherence theorems to facilitate manageable calculations in higher category theory.

Contribution

It introduces a new model structure for bigroupoids and pseudofunctors, with all objects cofibrant, and proves coherence theorems for these structures.

Findings

All objects in the model structure are cofibrant.

Coherence theorems for bigroupoids and pseudofunctors are established.

The coherence theorems may be of independent interest.

Abstract

A model structure on the category of (small) bigroupoids and pseudofunctors is constructed. In this model structure, every object is cofibrant. In order to keep certain calculations of manageable size, a coherence theorem for bigroupoids and a coherence theorem for pseudofunctors are proven, which may be of independent interest as well.