Contextual extensions of quantum gravity models

TL;DR

This paper introduces a categorical framework for incorporating contextual extensions into quantum gravity models, facilitating the development of topos-theoretic approaches to quantum gravity.

Contribution

It generalizes the concept of contextual extensions of $C^*$-algebras to quantum gravity models using category theory, enabling new structural insights.

Findings

Categorical limits of functors represent contextual extensions in quantum gravity models.

Provides a foundation for topos-theoretic quantum gravity models.

Generalizes existing algebraic structures to a categorical setting.

Abstract

We present a simple way of incorporating the structure of contextual extensions into quantum gravity models. The contextual extensions of $C^*$-algebras, originally proposed for contextual hidden variables, are generalized to the cones indexed by the contexts and their limit in a category. By abstracting the quantum gravity models as functors, we study the contextual extensions as the categorical limits of these functors in several quantum gravity models. Such contextual extensions of quantum gravity models are useful for building topos-theoretic models of quantum gravity.