Fibrations of topological stacks

TL;DR

This paper introduces the concept of fibrations for topological stacks, establishing their key properties, criteria, and examples, and connects these notions to classical fibrations in topology.

Contribution

It defines fibrations of topological stacks, proves fundamental properties, and shows how these generalize classical fibrations in topology.

Findings

Established properties of fibrations of topological stacks

Provided criteria and examples for fibrations

Connected stack fibrations to classical topological fibrations

Abstract

In this note we define fibrations of topological stacks and establish their main properties. We prove various standard results about fibrations (fiber homotopy exact sequence, Leray-Serre and Eilenberg-Moore spectral sequences, etc.). We prove various criteria for a morphism of topological stacks to be a fibration, and use these to produce examples of fibrations. We prove that every morphism of topological stacks factors through a fibration and construct the homotopy fiber of a morphism of topological stacks. When restricted to topological spaces our notion of fibration coincides with the classical one.