A New Approach to Quantising Space-Time: II. Quantising on a Category of Sets

TL;DR

This paper extends a novel space-time quantisation method to categories of sets, including causal sets and topological spaces, providing a framework for quantum theories of space-time structures.

Contribution

It applies a recent quantisation approach to categories of sets, broadening its scope to include causal sets and topological spaces.

Findings

Demonstrates quantisation procedure for categories of sets

Includes applications to causal sets and topological spaces

Provides a foundation for quantum space-time models

Abstract

In a recent paper by the author, a new approach was suggested for quantising space-time, or space. This involved developing a procedure for quantising a system whose configuration space--or history-theory analogue--is the set of objects in a (small) category $\Q$. In the present paper, we show how this theory can be applied to the special case when $\Q$ is a category of sets. This includes the physically important examples where $\Q$ is a category of causal sets, or topological spaces.