English

Morphisms (should be) everywhere

History and Overview 2025-06-11 v2

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 nn-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.

Keywords

Cite

@article{arxiv.2411.06806,
  title  = {Morphisms (should be) everywhere},
  author = {Attila Egri-Nagy and Miklós Hoffmann},
  journal= {arXiv preprint arXiv:2411.06806},
  year   = {2025}
}

Comments

15 pages, 2 figures, final version will be published elsewhere

R2 v1 2026-06-28T19:55:17.156Z