On a categoriacal theory for emergence

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.