Morphisms (should be) everywhere

TL;DR

This paper emphasizes the fundamental role of morphisms, or structure-preserving maps, across mathematics and intelligence, proposing a broad framework that distinguishes between dynamic and static morphisms for understanding various fields.

Contribution

It introduces a comprehensive framework for morphisms, differentiating between dynamic and static types, and highlights their universal applicability beyond mathematics to general intelligence.

Findings

Morphisms are fundamental tools in mathematics and intelligence.

A distinction between dynamic and static morphisms is proposed.

A flexible framework for understanding various fields using morphisms is outlined.

Abstract

Morphisms, structure preserving maps, are everywhere in Mathematics as useful tools for thinking and problem solving, or as objects to study. Here, we argue that the idea of operations being compatible across two domains goes beyond its mathematical use: it is a fundamental mechanism of any intelligence. We precisely define morphisms, distinguish between dynamic morphisms (on operations, binary relations) and static ones (on $n$-ary relations), and describe how a flexible and pluralistic use of morphisms can serve as a general framework for understanding and explanation in a wide variety of fields.