Pullbacks and Pushouts: Integration Points That Don't Lie
When two services need to agree on something, you need a pullback. When two sources need to merge, you need a pushout. Part 9 of applying category theory to Solutions Architecture.
🏷️ Software Architecture
10 posts tagged with Software Architecture
Products and Coproducts: The Algebra of Service Composition
API Gateways are products. Event routers are coproducts. Part 8 of applying category theory to Solutions Architecture—the universal patterns for combining and decomposing services.
Natural Transformations: Coherent Change Across Systems
When you change from one architecture to another, changes must be consistent everywhere. Part 6 of applying category theory to Solutions Architecture—the mathematics of coherent transformation.
Functors: The Mathematics of Migration
Every migration is a functor — a structure - preserving transformation between systems. Part 5 of applying category theory to Solutions Architecture, where we learn when migrations succeed and why they fail.
Why Your Services Don't Compose: A Diagnostic Framework for Integration Failures
When services don't work together, it's not random—it's one of four predictable failure modes. A practical guide to diagnosing and fixing integration problems using insights from category theory.
Composition as Architectural Law: Diagnosing Integration Failures
When services don't compose, it's not a bug—it's a mathematical impossibility. Part 4 of applying category theory to Solutions Architecture, where we develop a diagnostic framework for integration failures.
The Yoneda Perspective: Systems Defined by Their Interfaces
A system is completely characterized by how other systems interact with it. Part 3 of applying category theory to Solutions Architecture—the deepest insight in category theory, made practical.
Equivalence of Categories: When Different Architectures Are 'The Same'
A monolith and microservices can be mathematically equivalent. Part 7 of applying category theory to Solutions Architecture—understanding when radically different implementations are categorically identical.
Morphisms All the Way Down: API Design as Arrow-First Thinking
Stop designing services. Start designing contracts. Part 2 of applying category theory to Solutions Architecture—where we learn that the arrows, not the boxes, are the architecture.
The Categorical Solutions Architect: Viewing Architecture Through the Lens of Category Theory
Category theory isn't abstract nonsense—it's the formal language for the problems Solutions Architects already face. Part 1 of a series on applying mathematical foundations to real architectural challenges.
