Functors map logical relationships between domains while preserving their structure. The mathematical foundation that makes cross-domain reasoning possible — not by analogy, but by proof.
Categories define objects and the relationships (morphisms) between them. Education concepts, medical diagnoses, legal precedents — all expressible as categorical structures.
Systematic translations between functors that preserve compositional structure. How reasoning patterns transfer coherently between entirely different domains.
The deepest structural relationship between categories. Encodes the optimal trade-off between generality and specificity in reasoning.