Categorical Elegans: A Category-Theoretic Model of the C. elegans Nervous System

We present a complete category-theoretic formalization of the Caenorhabditis elegans nervous
system, the only organism with a fully mapped connectome. The hermaphrodite nervous system
comprises 302 neurons organized into 118 classes, connected by approximately 6,393 chemical
synapses and 890 gap junctions. We model this as a symmetric monoidal category C where ob-
jects are neurons and morphisms encode both chemical (directed) and electrical (symmetric) synaptic
connections. The neurotransmitter system defines a functor NT∗ : C → 2NT assigning acetylcholine,
glutamate, GABA, or monoamines to each neuron. Behavioral circuits (locomotion, mechanosen-
sation, chemotaxis, thermotaxis) emerge as distinguished subcategories with specific limit/colimit
properties. This categorification provides a rigorous mathematical foundation for computational
neuroscience and enables compositional reasoning about neural circuit function.