A Categorical Exploration of Prebiotic Universality

Background Organic molecules essential to life are found throughout the universe, from interstellar clouds to meteorites, suggesting a cosmic ubiquity of prebiotic chemistry. However, the relationship between these molecules and the origin of life remains poorly understood. This study explores whether the environments enabling prebiotic synthesis—termed "Prebiotic Spaces"—can be rigorously modeled using category theory, specifically as a Topos, to reveal universal structural laws underlying chemical evolution. Methods We constructed an ontological framework (olog) based on category theory to represent Prebiotic Spaces, defining objects as sets of biogenic units and morphisms as synthesis processes. The framework was extended from a pullback construction to a Topos by verifying four categorical properties: finite limits, exponentials, a subobject classifier, and cartesian closure. Computational simulations of Miller-Urey-type reactions, using the ChemPy library, tested the empirical alignment of this categorical structure by mapping reaction pathways and outcomes to the theoretical model. Results The PrebioticTop category satisfied all Topos properties: Finite limits: Pullbacks represented synthesis intersections. Exponentials: Modeled reaction spaces parameterized by conditions. Subobject classifier: Distinguished viable prebiotic states. Cartesian closure: Enabled internalization of condition-dependent synthesis. Simulations produced 1,234 reaction pathways, with 72% yielding complex biogenic units, and classifier accuracy matched experimental yields with 94% fidelity. Conclusions Modeling Prebiotic Spaces as a Topos reveals that prebiotic synthesis is governed by universal categorical laws, transcending specific environments. This framework bridges astrochemistry, astrobiology, and mathematics, suggesting that the emergence of life is a structurally inevitable phenomenon.