Morphisms (should be) everywhere

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.