The Evolution of Life as a Categorical Information-Handling Process

Abstract: Living systems can be understood as organized entities that capture, transform, and reproduce information. Classical gene-centered models explain adaptation through frequency changes driven by differential fitness, yet they often neglect the higher-order organization and causal closure that characterize living systems. Here we review evolutionary frameworks, from the replicator equation to group selection and holobiont dynamics, and show that evolutionary change in population frequencies can be expressed as a Jeffreys divergence. In holobionts, this formalism allows partitioning the total information associated with selection acting on the genome and the microbiome, as well as the information involved in matching specific genotypes with particular microbiotas, yielding an informational signature of stable symbiotic coevolution. Building on this foundation, we propose a categorical model of Information Handlers (IH), entities capable of self-maintenance, mutation, and combination. Each lineage is represented as a discrete coalgebra with internal (M,R) closure, while the global system forms a supercategory of interacting lineages. Replication, reproduction, and transmission are modeled as morphisms whose informational changes are captured by a functor mapping biological transformations into transformations within an informational category, measurable through Jeffreys divergences. This framework connects gene-centered evolutionary dynamics with relational and organizational perspectives, offering a unified categorical view of living systems.