On a categoriacal theory for emergence

TL;DR

This paper introduces a categorical framework to formalize and analyze emergent phenomena in biological systems, employing advanced mathematical constructs to better understand their complex nature.

Contribution

It develops a novel categorical theory of emergence using constructs, functors, and other category-theoretic tools, providing new insights into biological emergence.

Findings

Characterizes emergence through constructs and functors.

Establishes results on homomorphisms and categorical limits of emergences.

Connects the theory to biological system studies.

Abstract

It is well-known that biological phenomena are emergent. Emergent phenomena are quite interesting and amazing. However, they are difficult to be understood. Due to this difficulty, we propose a theory to describe emergence based on a powerful mathematical tool, namely, Theory of Categories. In order to do this, we first utilize constructs (categories whose objects are structured sets), their operations and their corresponding generalized underlying functor (which are not necessary faithful) to characterize emergence. After this, we introduce and show several results concerning homomorphism (isomorphism) between emergences, representability, pullback, pushout, equalizer, product and co-product of emergences among other concepts. Finally, we explain how our theory fits in studies involving biological systems.