Morphisms All the Way Down: API Design as Arrow-First Thinking
2 days ago
- #System Architecture
- #Category Theory
- #API Design
- Traditional architecture focuses on boxes (services, databases), while categorical architecture focuses on arrows (relationships, contracts).
- Morphisms in category theory represent relationships between objects and have more structure than objects themselves.
- Contract-first design is morphism-first design, where APIs are defined before implementation, making the implementation categorically invisible.
- Hom-Sets (Hom(A, B)) represent all possible morphisms between two objects, useful for analyzing integration points and coupling between services.
- The Principle of Minimal Morphisms advocates for minimizing hom-set sizes to reduce coupling while maintaining functionality.
- Composing morphisms allows for creating pipelines, enhancing testability, replaceability, and reasoning about systems.
- API versioning and breaking changes can be understood through the lens of morphism evolution and replacement.
- AWS services like API Gateway, EventBridge, and Step Functions can be viewed through the morphism lens as morphism transformers, composition engines, and state transitions.
- The key takeaway is to think in arrows (morphisms) rather than boxes, starting with contracts and letting objects emerge from morphism requirements.