Functors in Lorentzian geometry -- three variations on a theme

TL;DR

This paper reviews three functors in Lorentzian geometry, including a novel functor from ordered measure spaces to Lorentzian pre-length spaces, with applications in finiteness, singularity theorems, and boundary constructions.

Contribution

It introduces a new functor from ordered measure spaces to Lorentzian pre-length spaces, expanding the categorical framework in Lorentzian geometry.

Findings

Applications in finiteness results

Applications in singularity theorems

Applications in boundary constructions

Abstract

We review three examples of functors from Lorentzian categories and their applications in finiteness results, singularity theorems and boundary constructions. The third example is a novel functor from the category of ordered measure spaces to the category of Lorentzian pre-length spaces in the sense of Kunzinger-S\"amann.