On a Categorical Theory for Emergence

Emergent phenomena are quite interesting and amazing, but they present two main scientific obstacles: to be rationally understood and to be mathematically modelled. In this paper we propose a powerful mathematical tool for modelling emergent phenomena by applying category theory. Furthermore, since great part of biological phenomena are emergent, we present an essay of how to access an emergence from observational data. In the mathematical perspective, we utilize constructs (categories whose objects are structured sets), their operations and their corresponding generalized underlying functor (which are not necessarily faithful) to define emergence. From this definition, we elaborate several results concerning homomorphism between emergences, representability, pull-back, push-out, equalizer, product and co-product of emergences among other results. After we have presented such mathematical model, we utilize a hierarchical structure as example—from molecules to a flatworm—, in order to understand the relation between biological systems and its underlying emergence in a hierarchical model.