Model Perspective

Sep 20, 2026 · Fundamentals

Why Modeling Needs Category Theory: Turning 'Is This Model Right?' into Commutative Diagrams

This article explains how category theory addresses three core modeling challenges—verifying correctness, composing models, and maintaining consistency across abstraction layers—by using commutative diagrams to define model validity, functors to preserve structure across representations, and pullbacks to enforce interface compatibility, with examples from numerical analysis, unit conversion, and fluid-structure coupling.