Taking Cognition Seriously: A generalised physics of cognition

TL;DR

This paper advocates applying category theory to model cognition, revealing physical trade-offs and proposing requirements for cognitive categories, while exploring topological defects in gauge fields over conceptual spaces.

Contribution

It introduces a category-theoretic framework for cognition, linking physical trade-offs to cognitive structures and analyzing topological phenomena in conceptual spaces.

Findings

Physical trade-offs in compact cognitive systems.

Requirements for defining cognitive categories.

Topological defects in gauge fields over conceptual spaces.

Abstract

The study of complex systems through the lens of category theory consistently proves to be a powerful approach. We propose that cognition deserves the same category-theoretic treatment. We show that by considering a highly-compact cognitive system, there are fundamental physical trade-offs resulting in a utility problem. We then examine how to do this systematically, and propose some requirements for "cognitive categories", before investigating the phenomenona of topological defects in gauge fields over conceptual spaces.